Prepare the dough. In a bowl, thoroughly mix water, egg and salt until smooth, beating them with a fork for about 4-5 minutes. Start adding flour, stirring the dough with each new portion: first with a spoon, and when it begins to thicken - with your hand. The dough must be thoroughly kneaded, grabbing from the edges to the center. After that, cover it with a towel and put it in the refrigerator for 30 minutes. During this time, it will become elastic and pliable.
While the dough is in the refrigerator, prepare the filling. Finely chop the onion. Fry over medium heat until translucent, about 4 minutes. Add the sauerkraut, stir, cover and simmer for 20-30 minutes. Transfer to a plate and let cool.
While the filling is cooling, prepare the frying for the finished dumplings. Finely chop the onion and fry it over medium heat for about 5 minutes until golden brown. Remove from heat.
Start making the dumplings. Sprinkle a little flour on the table, take the dough out of the fridge, roll it out with a rolling pin into a layer about 1 mm thick. Take a glass or cup and cut small circles. Roll the rest of the dough into a "sausage", cut into small pieces and roll the circles by hand.
Place the filling in the center of each circle and pinch the edges. The seam should be tight enough to prevent it from falling apart.
Boil the dumplings. Throw them into the water and stir with a slotted spoon so that they don’t stick to the bottom. After about 2 minutes, as soon as the dumplings float to the surface, take them out and serve.
Serve the finished dish, pouring the fried mixture on top. You can also sprinkle the dumplings with chopped green onions and add a couple of pieces of lard.