Combine the feta cheese, hot sauce, and one egg in a medium-sized bowl and whisk until thoroughly combined; set aside.
For the Pierogies
Combine the flour and sour cream in your mixer's bowl; mix with the dough hook until you have a soft ball of dough. If too wet, add a tablespoon of flour, if too dry, add more sour cream, one tablespoon at a time.
Lightly flour your working station and turn out the dough.
Roll out the dough to a 1/4-inch thickness. Use several passes to roll it to the desired thickness. Don't try to flatten it with just one pass.
Using a 3-inch round cookie cutter, cut dough into 20 rounds, rerolling the scraps as needed.
Place filling into the center of each round and fold in half, closing the edges with the tines of the fork. Be sure all edges are sealed.
In a large skillet or saucepan, heat the oil to 350˚F.
Place 2 to 3 pierogies in the hot oil and cook for 2 minutes, or until the pierogies float to the top and the edges start to brown; flip and cook for another minute or two, or until completely browned.
Remove and drain on paper towels.
Serve the pierogi plain or with sour cream, caramelized onions, or salsa.
Notes
Don't overfill the pierogi. You only need about one tablespoon of filling inside each dumpling. Any more than that, and you risk the filling oozing out.
The pierogi dough should be smooth and stretchy. Add extra flour or sour cream if necessary.
Make sure the pierogi are completely sealed at the seams before frying them.
Don't crowd the skillet - fry them in batches.
Storing and Reheating Leftovers: Cool the fried pierogi, then put them in a container or sealable bag. Keep in the fridge for up to 5 days. Warm them in a skillet with a bit of oil. If you use a microwave, they may be less crispy.
Freezing Pierogies: Cool, then freeze the pierogi on a baking tray. Once solid, store them in a container or freezer bag and keep them frozen for up to 3 months. Thaw in the fridge and reheat as usual.