Place potatoes in a large pot, cover with water, and bring to a boil. Simmer until fork-tender, about 15 minutes. Drain and mash the potatoes. Let cool completely.

In a small skillet, heat olive oil over medium heat. Sauté chopped onion until tender. Let cool.

Rinse sauerkraut thoroughly under running water for at least 3 minutes. Drain very well.

In a bowl, combine the cooled mashed potatoes, sautéed onions, drained sauerkraut, and farmer's cheese. Mix well. Refrigerate until ready to use.

In a large bowl, whisk together flour and salt. Make a well in the center and crack in the egg. Gradually add hot water, mixing with your hands until a sticky dough forms. Add a little more flour if too wet, or a tiny bit more water if too dry.

Cover the bowl and refrigerate the dough for at least 1 hour.

Bring a large pot of salted water to a rolling boil.

Lightly flour a clean surface. Divide the dough into 4 portions. Roll out one portion thinly (about 1/8-inch thick). Cut out circles using a round cutter (about 3 inches in diameter).

Place about 1 tablespoon of filling onto one half of each dough circle. Fold the dough over the filling to create a half-moon shape. Pinch the edges firmly to seal. Place prepared pierogi on a lightly floured tray, ensuring they don't touch.

Carefully drop pierogi into the boiling water, a few at a time, making sure not to overcrowd the pot. Stir gently to prevent sticking. Cook until they float to the surface, then let them boil for an additional 2-3 minutes.

Remove cooked pierogi with a slotted spoon. You can serve them boiled, or for a crispier texture, melt butter in a skillet over medium heat and pan-fry the boiled pierogi until golden brown on both sides.

Serve hot, drizzled with melted butter and your favorite toppings like sour cream or applesauce.