Boil the potatoes in their skin until soft. Depending on the size, this takes about 20 minutes. Check for doneness by piercing the potato with a fork. If the potatoes are soft, they are cooked. Drain the water and let them cool completely.
Peel the cooled potatoes and grate them finely on a box grater. Add an egg, flour, and salt.
Work into a compact dough. First, roughly mix all the ingredients in a bowl using a fork. Then dump the mass onto a floured work surface and knead until the dough does not stick.
If the dough is too sticky, dust it with a tablespoon of flour and work it in. Continue like this until the dough holds together nicely and does not stick to your hands.
Divide the dough into three to four pieces. Roll each of them into a cylinder. Cut off equal-sized pieces and roll them into a šiška shape about the size of your index finger.
Meanwhile, take a wide pot, pour water into it, add 1 tsp salt and let it boil on the stove. Turn down the heat so that the water simmers.
Carefully drop šišky into the water. They will stick to the bottom; gently peel them off with a spatula. Once the šišky have floated to the surface, cook for two more minutes. Transfer them to a shallow bowl using a colander or a slotted spoon. The whole cooking process takes about 10 minutes.
Fry the breadcrumbs with sugar: Melt unsalted butter in a frying pan over medium heat. Pour in the breadcrumbs; stir. The breadcrumbs should turn golden within five minutes—if not, increase the heat slightly. Remove the pan from the heat and add granulated sugar to the breadcrumbs. Stir well.