Peel the potatoes and boil them until ready in salted water. Discard the remaining water, mash the potatoes and cool them.
Add finely chopped dill and cheese, grated ahead of time on a coarse grater.
Spread out each slice of ham. Put potato filling at one end and wrap it into a roll.
Dip each roll in the beaten egg.
Arrange the ham rolls in a tray laid out with baking paper.
Bake in a preheated 392°F (200 °C) oven.
Serve the dish warm.