Peel the asparagus and place in a saucepan with water. Add a tablespoon of milk, a little salt, sugar and lemon juice, cook the asparagus until al dente.
Boil the potatoes including the skin in a saucepan with salted water until they are al dente.
Preheat the oven to 210 degrees.
Put the butter in a gratin dish and let it melt in the oven, the butter should be nut brown. Cut the asparagus into 4-5 cm long pieces, peel the potatoes and cut into thin slices, mix the asparagus and potatoes in the gratin dish.
Beat the eggs with the rest of the milk, mix the herbs, cheese and a little pepper into the egg mixture. Pour the whole thing over the mixed asparagus and potatoes and bake in the oven for 10 minutes.