Peel the asparagus and cut into pieces. Peel and wash the potatoes. Cook the asparagus with the potatoes in salted water with a pinch of sugar for 15-20 minutes.
Melt the butter in a pan, about 1 tablespoon. Stir in freshly ground pepper. Drain the asparagus and potatoes well, add both to the pan and toss until everything is coated with butter, then transfer to the plates.
Fry the eggs in the butter, pepper and salt.
Let the eggs slide onto the asparagus and potato vegetables.