This dish is really a 3 step dish. Don't be disheartened because step one is the most complicated, but trust me, once you've made this once, you'll actually wonder why you haven't made your own fresh pasta all of your life so far!
Step 1: You need to make some fresh pasta. Of course, you can buy this pretty affordably in the shops if you like, or you could buy the dried stuff even cheaper still, and it'll stay in your cupboard for ages. Personally, with fresh free range eggs literally at the end of my garden, I like to make as much of this, and indeed any dish, as possible, from scratch. And if you make a batch of pasta in one go, you've effectively created half of the next evening's meal already, in advance, for barely any extra effort.
Start by getting a largish bowl and add in some pasta flour. I tend not to use measurements but go by what feels right, as even the size of an egg can make a difference to this mix. However, I would say to aim for about 1/5th of a packet of fresh pasta flour as a starting point and this should be more than enough for this dish and probably some pasta left over for the next day too.
In the bowl, with the flour now added, make a 'well' in the middle and crack a couple of egg yolks into it. Don't panic if the whites ooze in a little too, but the more yolk and less white you get in here, the better the pasta will bind and the nicer the colour will look.
Then, with a fork, whisk the egg yolk together. Once the yolk is one yellow puddle in the centre of the bowl, add in a dash of decent quality olive oil. Other recipes suggest maybe a tablespoon or so. Me? I give it a good glug, and I always try and use the proper Italian Olive Oil for this too. It makes me feel like I am creating a proper Italian dish this way. Then, start drawing in the flour from around the yolk and oil and mixing together. It'll get sticky and stiff the more you bring it together. Don't panic if it looks too wet or too dry, as you can add more oil or flour if necessary later.
But, after a while, you should start to see the mass become more solid and at this point, with clean hands, you may be able to start to handle it as a more solid ball. Pour a little more flour on your worktop and roll the pasta, if it's formed enough, into a sort of 'dough ball' in your hands and then kneed the ball through the flour on the counter. As the pasta absorbs the flour (not too much, you don't want the pasta going to dry or flourery) it should become more workable until after 10 minutes or so, you should have a nice yellow ball shape of pasta. Wrap this in clingfilm and plonk in your fridge for a bit whilst you prepare the rest of the dish.
Step 2: This is the good bit. In a frying pan over medium high heat, add some oil and then add some chopped onion and garlic. Reduce heat slightly and keeping turning the onions and garlic as you don't want the garlic to burn.
After a few minutes, add in the mushrooms, peppers too if you fancy it and keeping stirring. If the pan is looking too greasy, I like to deglaze at this stage with a little red wine...add a splash, and the pan with spit and steam a but but the fat and oil will evaporate and burn off. Once the dish is less oily, then add in the tin of chopped tomato, along with seasoning - parsley, salt and pepper, chilli flakes and oregano - take your pick to suit your taste!
After a while, the water content from the tomatoes should also start to reduce. If not, turn up the heat a tad. Or add more red wine. Personally, I like to add a few chocolate drops and tomato puree at this stage to properly thicken the mixture and add a great depth of flavour.
Then, once the dish looks like a mince dish, rather than a sloppy mess, reduce the heat to a minimum or turn off altogether.
Step 3: Roux sauce. This is one element of cooking that sounds sooooooo complicated but is actually incredibly easy. You'll never need buy a packet sauce again. However, preparation is key to this stage because once you start the process, you don't want to leave the dish and start hunting for the components. Start by grating a handful of cheese and getting the milk out of the fridge. Get yourself a wooden spoon at the ready and cut a few knobs of butter and add them to a clean saucepan.
Then, put the pan on a medium hob heat. The butter should start to melt but make sure you aren't cooking the butter. You just want to melt it. Then, when it is all liquified, add in some flour. The idea is, to create a sort of paste between the flour and the butter. Like a sticky looking butter I guess. I normally take the pan off the heat at this stage.
Once you've created a paste, return to a gentle heat and pour in some milk, a little at a time and keep stirring the whole mixture. Don't worry about lumps to start with but fairly soon the paste will absorb the milk, and you can add more. If the heat is too warm or if you don't add enough milk, the paste will become very dough like again. So keep adding milk, but only in dribs and drabs and keep stirring. Turn up the heat slightly if need be but don't boil the mixture!
After a while, the mixture will thicken and when it does, you can start to introduce the cheese, as well as topping up with more milk and continuing to stir. The cheese too should melt and become part of the sauce.
The roux sauce for lasagne is slightly different from the roux sauce for say mousakka because with mousakka, I normally add in a broken egg right at the end and mix in to give a different texture to the sauce. But you can still do this with this sauce if you like as well.
Bring it all together: Ok, so now you have made your basic pasta and it's chilling in the fridge, the meat and filling is done and the sauce is sat ready to go in to the dish.
You now need to roll out your pasta. If you have a pasta machine, this is a quick and easy task. If not, a rolling pin and floured counter will work too. You don't want pasta that is too thick here but not too thin either. You ideally want or need to be able to handle it and to create rectangular shapes that fit the shape of your lasagne dish perfectly. Don't worry if not, as you can add different sizes and shapes of the pasta to make a sort of patchwork if need be and nobody will ever know the difference, trust me ;)
Whilst all this is going on - set your oven to about 190 degrees without a fan (fan can make the sauce bubble too much in my opinion). Find yourself a nice dish a couple of inches deep ideally and spoon in a layer of mince mixture. About a third of it. Then add sauce over the top of this. Don't mix the sauce and the mince with a spoon but just pour over. Then add a layer of pasta. Then do the same all over again; mince, sauce, pasta. The last layer 'looks best' when having a little meat with a little sauce over the top.
Once the dish is whole, plop into the oven and leave for maybe 25 minutes. It's fairly easy to see when done as the top layer of sauce should start to crisp and colour a bit. If it does this too quickly, turn the heat down or move the dish to a lower shelf. The dish needs time to cook so the pasta, the only real raw ingredient, cooks in the sauce and the mince.
Once done, bring out of the oven, being mindful that the dish will be VERY hot and place on a trivet to cool for a minute or two, before dividing up and serving.