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.
Combine the mashed potatoes and cheese, and then season with salt and pepper.
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.
Heat the butter in a large skillet over medium heat. Butter will foam, then settle down. Continue to cook until the butter just begins to brown and develop a toasty, nut aroma.
Add the pierogi to the skillet with the butter and sear each side for about 1 minute or until golden. Serve warm.
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