Cut the onion into strips and sauté with a little oil in a non-stick pan. Add the chopped artichokes, the peas and the coarsely chopped spinach. Season with salt and pepper and sauté for a few minutes, stirring occasionally.
Heat the milk, nutmeg and a pinch of salt in a small saucepan, bring it to the boil and set it aside.
Melt the butter in a saucepan, add the flour and stir in with a whisk. Sauté the roux over medium heat for a few minutes, stirring constantly.
Gradually whisk in the milk to make a compact Béchamel sauce without lumps, let it simmer over low heat for a minute, stirring constantly and making sure it doesn't stick to the bottom. Remove from the heat and stir in the “Stelvio PDO” or "Pusteria" cheese.
Put a layer of Béchamel sauce on the bottom of a casserole dish and place two sheets of fresh egg pasta on top. Spread another layer of Béchamel sauce on top and add some vegetables. Continue layering until all the ingredients are used up. Sprinkle the surface with grated hard cheese and spread a few small pieces of butter on top.
Bake the lasagna in a preheated oven at 180°C (160°C convection oven) for 35-40 minutes, until it is gratinated on the surface.
After removing from the oven, let it rest for 5 minutes, then portion and serve.