Make the pierogi dough. Place the flour and salt in a large bowl. Combine the vegetable oil and water in a glass measuring cup. Add three quarters of the water and oil to the dry ingredients and start to combine the ingredients with your hand until a dough comes together. Add more liquid if needed in order to get the dough to come together, or a little more flour if your dough is too sticky and wet. You’ve added just the right amount of liquid if the bowl is almost clean when you’ve finished stirring the dough together. Knead the dough lightly for about 5 minutes and then set it aside to rest for at least 10 to 15 minutes.

While you wait for the dough to rest, peel and cut the potato into three large chunks. Boil the potato in salted water. When it is tender and almost falling apart, strain the potato and return it to the hot saucepan. Crush the potato with a fork or potato masher and add the grated Cheddar cheese, working it in and letting it melt as you mash the potato. Season to taste with salt and freshly ground black pepper and set this mixture aside to cool slightly.

Divide the rested dough into four portions. Then, roll each portion lightly into a log with a diameter of about 1½-inches. Divide each roll of dough into six pieces. Flatten and roll each piece of dough into a circle (or as close to as possible). Flatten with your hand first and then use a rolling pin to roll the dough into a disk about ¼-inch thick with a diameter of about 4-inches.

Place about a tablespoon of cheesy potato mixture in the center of each disk and fold the dough over the filling. Pinch the edge together firmly with your fingers. Then, go around the edge pinching again to make sure the seal is secure. Set the filled pierogies aside. (If you don’t plan to cook them right away, store them in the refrigerator, well-covered with plastic wrap or a clean kitchen towel. You can also freeze the pierogies at this stage – freeze them on a baking sheet and then transfer the frozen pierogies to an airtight bag once frozen.)

Before you cook the pierogies, Heat a large skillet or sauté pan over medium heat. Add the butter and the sliced onions and cook the onions slowly for about 20 minutes. The onion should be tender and lightly browned.

To cook the pierogies, bring a large pot of salted water to a boil. Drop the pierogies into the boiling water. (Do this in two batches – about 12 at a time in a large stockpot.) When they come to the surface and float (about 2 to 3 minutes), give them just 30 seconds longer and then remove them with a slotted spoon. Transfer the pierogies to the skillet with the butter and onions. You can increase the heat and fry the pierogies if you like, or just toss them with the onions. Hold them warm in a 170ºF oven or serve immediately with sour cream and chopped scallions or however you like ‘em!