Drain: Place the cottage cheese into a fine-mesh sieve and drain thoroughly.
Toast breadcrumbs: Start by preparing the breadcrumbs. Melt the butter in a large pan, add the breadcrumbs and stir for a few minutes until the breadcrumbs are golden. Transfer to a large bowl and let them get cool. When cold, add the sugar and mix well.
Bring a large pot of water to a boil. Add the salt.
Combine: In the meantime, mix the drained cottage cheese, egg, and vanilla sugar in a bowl. With the immersion blender, blend the ingredients until you obtain a rough paste. Add the semolina and the flour and mix with a spoon. The dough should be soft and a little bit sticky but still manageable.
Dough: Sprinkle the working surface generously with flour. Turn the dough onto the flour and form a ball. If the dough is too soft and you cannot really work with it, gradually add a little more flour. Don't overdo it, or the dumplings will turn out too tough. The dough should be very soft, and it is ok if it is still a bit sticky.
Make dumplings: Flour your hands and form a sausage, about 3-4 cm/ 1.1 – 1.5 inches in diameter. Cut the sausage into about 20 pieces. With floured hands, roll each piece into a ball. Turn this ball very lightly through the flour on the working surface (only if it's highly sticky), shake to remove the excess flour, and press into a disc. With a floured finger, press a small dent in the middle of the dumpling.
Cook dumplings: When the water is boiling, turn the heat down to medium-low. Place all the dumplings into the pot. They will sink to the bottom of the pan, so take a slotted spoon and go under the dumplings to prevent them from sticking to the pot. After a few minutes, the dumplings will come up. Cover the pan and simmer gently for about 5 minutes. Then, turn off the heat and let the dumplings in hot water for another 5 minutes.
Coat with breadcrumbs: Remove dumplings with a slotted spoon, drain them in a sieve and roll each dumpling in the breadcrumb mixture. Serve warm as they are or topped with some runny jam.