1. Make the Dough:
In a large bowl, combine flour, salt, beaten eggs, oil, and about 1½ cups cold water. Mix to form a dough, adding more water if needed. Knead on a floured surface for 4–5 minutes until smooth and pliable. Cover with plastic wrap and let rest at room temperature for 30 minutes to 1 hour.

2. Prepare the Filling:
Peel and cut potatoes into 2-inch cubes. Boil in salted water for approximately 15 minutes until tender. Meanwhile, sauté finely diced onions in half of the butter over medium-low heat until soft. Drain potatoes and mash until smooth. Mix in cooked onions, shredded cheddar cheese, remaining butter, salt, and pepper until very smooth. Cool completely.

3. Assemble Pierogies:
Divide dough in half. Roll out one half on a floured surface to about ⅛-inch thickness. Use a 3-inch round cutter to cut circles. Place about 1 ½ tablespoons of filling in the center. Fold into a semi-circle, pressing edges firmly. Repeat.

4. Cook Pierogies:
Bring a large pot of salted water to a boil. Add pierogies in batches without crowding. Cook until they float, about 2–4 minutes. Transfer to a skillet with melted butter, frying until golden.

5. Serve:
Serve warm with sautéed onions and optional sour cream. Garnish with herbs if desired.

6. Freezing:
Place assembled pierogies on parchment-lined sheets, freeze until solid. Transfer to zippered bags for up to 4 months. Cook frozen by boiling until floating, then fry as usual.