How to Make It
In a bowl, mix together the flour, sour cream, egg, olive oil, and salt until the ingredients bind together. Place the dough on a lightly floured surface and knead for a couple minutes, or until smooth. Wrap in plastic wrap and let rest for 30 minutes.
Place the potatoes and 1/2 teaspoon salt in a large pot and fill with cold water to cover the potatoes. Bring the water to a boil over high heat, then reduce heat to medium-low and then simmer for 10-15 minutes or until the potatoes are tender when pierced with a fork. Drain potatoes and mash. Allow to cool.
In a skillet, heat the olive oil over medium-high. Stir in the mushrooms and cook for 3 minutes or until soft. Stir in Worcestershire sauce and season with black pepper. Combine the mashed potatoes, mushrooms and feta cheese. Set aside.
Preheat the oven to 375°. Line a baking pan with parchment paper.
On a lightly floured surface, roll out the dough to about 1/8-inch thick. Using a 3-inch round cutter, cut out 12-15 rounds. Brush the edges of each round lightly with water, then place 1 tablespoon of filling on one side of the rounds. Fold the dough over, making half moon shapes, pressing out the air. Press and crimp the edges to seal the pierogi.
Bring a large pot of salted water to a rolling boil. Cook the pierogi for 3-5 minutes, or until tender. Drain and brush the pierogi with olive oil.
Place the pierogi on the lined baking pan and bake for 15 minutes or until crispy. Serve hot.