Wash and peel the asparagus and cut off the woody ends generously. Cut the asparagus into thin, diagonal slices. Add boiling salted water with some sugar to approx. 1⁄4 l boiling water, bring to the boil, cover and simmer for approx. 3 minutes. Drain, catch the asparagus stock. Take the pasta dough out of the fridge.
For the sauce, peel onion and garlic and dice finely. Heat 4 tablespoons of butter in a saucepan. Sauté onion and garlic. Dust with flour and sauté until light brown. Stir in almost 200 ml asparagus stock, milk and broth. Bring to the boil, cover and simmer for about 5 minutes. Season to taste with salt, pepper and nutmeg. Add asparagus to the sauce.
Grease an ovenproof dish (approx. 30 x 35 cm) and spread some sauce on the bottom. Halve the pasta dough and put one half in the baking dish. Spread half the sauce on top. Pile the rest of the pasta dough and sauce on top. Dice mozzarella, grate parmesan and spread both on the asparagus lasagne. Bake in the preheated oven (electric cooker: 200 °C/circulating air: 175 °C/gas: see manufacturer) for approx. 40 minutes until golden brown.