Preparing the Dough

1. Mix the Dry Ingredients: In a large mixing bowl, combine the flour and salt.
2. Add Wet Ingredients: Create a well in the center of the flour mixture. Pour in the warm water, beaten egg, and vegetable oil.
3. Knead the Dough: Stir the ingredients together until a dough forms. Transfer it to a floured surface and knead for about 10 minutes until the dough is smooth and elastic.
4. Rest the Dough: Cover the dough with a damp cloth or plastic wrap and let it rest for at least 30 minutes. This allows the gluten to relax, making it easier to roll out.

Preparing the Filling

5. Cook the Potatoes: Boil the cubed potatoes in salted water until tender, about 15-20 minutes. Drain and set aside.
6. Sauté the Onion: In a skillet, melt the butter over medium heat. Add the chopped onion and sauté until golden brown.
7. Mash the Potatoes: In a large bowl, mash the cooked potatoes. Stir in the sautéed onion, cottage cheese, shredded cheddar cheese, salt, and pepper. Mix until well combined.

Assembling the Varenyky

8. Roll Out the Dough: On a floured surface, roll out the dough to about 1/8 inch thickness. Use a round cutter or a glass to cut out circles, approximately 3 inches in diameter.
9. Fill the Dough Circles: Place a spoonful of the potato and cheese filling in the center of each dough circle.
10. Seal the Dumplings: Fold the dough over to create a half-moon shape. Press the edges firmly to seal, using a fork to crimp the edges for extra security.

Cooking the Varenyky

11. Boil the Dumplings: Bring a large pot of salted water to a gentle boil. Carefully drop the varenyky into the water in batches, stirring occasionally to prevent sticking.
12. Cook Until Done: Once the varenyky float to the surface, continue cooking for an additional 2-3 minutes.
13. Drain and Serve: Use a slotted spoon to remove the varenyky. Drain well and transfer to a serving dish.