Peel the potatoes and cook them in salted water. Cut off the lower third of the asparagus. Cut off the asparagus heads and set aside, cut the stalks into thin slices. Bring some water with a pinch of sugar and a little salt to the boil. Add the asparagus pieces and cook until just under cooked, drain and keep warm.
Briefly fry the asparagus tips in a pan with a little butter.
Drain the potatoes, add milk, butter and nutmeg and mash with the potato masher. Season with salt, pepper and nutmeg. Fold in the asparagus pieces.