Place the flour in a large kitchen bowl.
In the center of the flour, make a well, as if you were beginning to make pasta. In the well, incorporate the water, egg, oil and salt.
Begin lightly beating the egg mixture, while moving the fork slowly from the middle of the bowl, gradually incorporating the flour until a soft dough forms.
Once all of the flour is incorporated and the dough is formed, remove the dough to a lightly floured, clean, dry countertop. Knead the dough, dusting with flour as needed to prevent sticking to the countertop.
Loosely cover the dough with plastic wrap and allow to rest at room temperature for 1 hour.
Roll out the dough to a 1/8-inch thickness. Take a 2 1/2- inch round cookie cutter and cut circles out of your dough. Select the Thanksgiving fillings of your choice. (See below)
Place a good-size tablespoon of filling in the middle of the circle of dough. Fold into a half moon and pinch the edges.
You can either cook them now or freeze them for later.
To freeze, do NOT cook them first. Place the pierogies on baking sheets for three hours in the freezer so they do not touch. Once frozen, place all of them in a ziptop bag for future use.
To cook, boil salted water in a medium to large saucepan. Boil the pierogies in batches for about 5 minutes or until they float. Once they float, they are ready to eat.
If you want, after boiling, you can saute the pierogies in brown butter for a nice finish.
For the Filling:
Potatoes: Mix up cold mashed potato with a little nutmeg. You can also chop up some leftover Brussels sprouts to add to the mashed potato.
Turkey: Combine shredded turkey with a little cheese (such as Brie) and leftover cranberries. Or leave plain.
Sweet Potatoes: Mix sweet potatoes with sausage (such as chorizo), if you have some. It is also good with curry and leftover peas. If you want a sweet potato pie flavor, add nutmeg and cinnamon to the sweet potato and dust the pierogies with powdered sugar.
Proceed to fill dough and bake or freeze.