MAKE THE PIEROGI DOUGH: In a large bowl, mix the flour with the sour cream, egg, egg yolk, butter and salt. On a lightly floured work surface, knead the dough briefly until smooth. Cover the dough with plastic wrap and let rest at room temperature for 15 minutes.
MEANWHILE, MAKE THE FILLING: In a medium saucepan, cover the potatoes with water and boil until tender, about 12 minutes. Drain the potatoes and peel them as soon as possible. In a bowl, mash the potatoes with the sour cream, mustard and 2 1/2 tablespoons of the butter until smooth. Season with salt and pepper.
Bring a large pot of salted water to a boil. On a floured work surface, roll out the pierogi dough „ inch thick. Using a 3 1/2-inch biscuit cutter, stamp out 20 rounds. Brush off any excess flour and moisten the edge of each round with water. Place a level tablespoon of the potato filling on one side of each round, leaving a 1/4-inch border. Fold the dough over the filling to form half-moons and press the edges firmly to seal.
Cook the pierogies in the boiling water until tender, about 5 minutes. Drain well and transfer to a large, shallow dish. Add a little vegetable oil and toss to coat lightly.
In a large skillet, melt the remaining 1 1/2 tablespoons of butter. Add the pierogies and cook over moderate heat, turning once, until browned, about 3 minutes per side. Transfer the pierogies to a platter. Season with salt and pepper, sprinkle with the parsley and serve.
MAKE AHEAD The pierogies can be prepared through Step 4 and refrigerated for up to 3 days.