Step 1: Make the dough by combining flour and salt in a bowl. In another bowl, whisk egg, water, and sour cream. Gradually mix wet ingredients into dry until a dough forms. Knead for 5 minutes until smooth, wrap in plastic, and rest for 30 minutes.
Step 2: Boil potatoes in salted water until tender, about 15 minutes. Drain and mash with butter, farmer’s cheese, cheddar, salt, and pepper until smooth. Let cool.
Step 3: Roll dough on floured surface to 1/8-inch thickness. Cut into 3-inch circles with a cookie cutter or glass.
Step 4: Place 1 tablespoon filling in center of each circle. Fold dough over filling to form half-moon shape, pressing edges firmly to seal. Crimp edges with a fork if desired.
Step 5: Bring a large pot of salted water to boil. Cook pierogi in batches for 3-4 minutes until they float. Remove with slotted spoon.
Step 6: In a large skillet, melt butter over medium heat. Add onions and cook until golden, about 5 minutes. Add boiled pierogi and pan-fry for 2-3 minutes per side until lightly browned.
Step 7: Serve hot with sautéed onions and sour cream on the side.