Wash and peel the asparagus and cut off the woody ends. Cook in boiling salted water for about 18 minutes. Meanwhile, peel and wash the potatoes and cook in boiling salted water for about 20 minutes. Clean and wash the broccoli, cut off the florets and cook in boiling salted water for about 10 minutes. Heat milk and herb butter. Remove the asparagus from the water and drain. Drain the potatoes, mash them with a potato masher and mix with the warmed milk.
Season to taste with salt, pepper and nutmeg. Drain broccoli and fold into the mashed potatoes. Mix crème fraîche and egg and season with salt and pepper. Pour the mashed potatoes into a greased casserole dish, spread the asparagus on top, pour crème fraîche on top and sprinkle with cheese. Bake the casserole in a preheated oven (electric: 200 °C/ gas: level 3) for 15-20 minutes. Serve sprinkled with chervil and pepper to taste