Lasagne, whether they're with ragù or veggie, are extremely comforting, part of that comforting deriving from the long process needed to make them. I would recommend preparing the ragù the day before, and the fresh pasta and béchamel just before you assemble the dish.
1. Make the ragù the day before or at least the morning of your chosen lasagna day (if you're making them for dinner). Follow my ragù recipe here.
2. Place the flour onto a wooden surface and form a well in the middle, crack in the whole eggs and being whisking them slowly with a fork. Little by little, begin incorporating some flour and whisking. Once it becomes too thick to handle with a fork, begin kneading it with your hands, for roughly 10 minutes, until you achieve a smooth and compact dough. Wrap it in cling film and set it to one side as you prepare the béchamel.
3. Melt the butter in a deep pot and begin adding the flour, little by little, mixing with a whisk to make sure there are no lumps. Turn the heat up and pour in the milk little by little, mixing with a wooden spoon. Once you've poured in all the milk, keep mixing until the sauce becomes denser. The consistency you're aiming for is when you draw a line with your finger on the back of the wooden spoon covered in sauce and the line stays clear. Turn off the heat and add in three handfuls of grated parmigiano and a sprinkle of nutmeg, mixing well.
4. Roll out the dough with a pasta machine the thinnest possible, then measure the length of the baking tray you're using and cut pasta accordingly.
5. Bring a pot of water to boil, add salt and begin cooking each piece of pasta, by itself, for 3 minutes each. Once cooked, scoop out of the pot and place on a kitchen towel to dry off.
6. As the pasta boils, grate your mozzarella and have it ready for use.
7. Once all your pasta is cooked, you can begin assembling your lasagna. In a bowl, mix together 3 tablespoons of ragù and 3 of béchamel, then spread it evenly over the bottom of the baking tray. Cover well with the pasta, then add another mix of béchamel and ragù, and 2 handfuls of grated mozzarella. Cover with pasta again. Repeat the process for at least 5 layers of pasta, then add béchamel, ragù, mozzarella and some grated parmigiano on top of the last layer.
8. Preheat the over to 180° Celsius and bake for 25 minutes.