Make the dough Stir together flour and salt in a large bowl; make a well in the center. Add egg yolk and butter; gradually add ⅔ cup warm water, and stir using your hand until a shaggy dough forms.

Bring dough together to form a ball. Turn dough out onto a lightly floured surface, and knead until smooth, 6 to 7 minutes. Wrap dough in plastic wrap; let rest 20 minutes.

Meanwhile, make the filling Heat oil in a large skillet over medium. Add cabbage, and cook, stirring occasionally, until wilted, 2 to 3 minutes. Drizzle with 1 tablespoon water. Reduce heat to low; cover and cook until cabbage is tender, about 10 minutes. Transfer cabbage to a large bowl; set aside. Wipe skillet clean.Meanwhile, make the filling: Heat oil in a large skillet over medium. Add cabbage, and cook, stirring occasionally, until wilted, 2 to 3 minutes. Drizzle with 1 tablespoon water. Reduce heat to low; cover and cook until cabbage is tender, about 10 minutes. Transfer cabbage to a large bowl; set aside. Wipe skillet clean.

Cook bacon in skillet over medium, stirring occasionally, until rendered and crisp, 6 to 8 minutes. Transfer about half of cooked bacon to a small paper towel–lined bowl; set aside for garnish. Add onion to remaining bacon in skillet. Cook over medium, stirring occasionally, until onion is softened and golden, 6 to 8 minutes. Add onion mixture, white pepper, and salt to bowl with cabbage; stir to combine. Let cool 10 minutes. Stir in feta and egg until well combined. Set aside.

Roll dough out on a lightly floured surface to about ⅛-inch thickness. Cut out circles using a 3-inch round cutter or rim of a 3-inch round drinking glass, rerolling scraps until all dough is used.

Working with 1 dough round at a time, place about 1 tablespoon filling in center of circle; fold dough in half to form a half-moon shape. Press edges tightly to seal, pressing out any air. (If edges open, use a bit of water to help reseal.) Crimp edges using a fork. Place filled pierogi on a lightly floured baking sheet; cover loosely with plastic wrap or a clean kitchen towel. Repeat process with remaining dough rounds and filling.

Bring a large pot of salted water to a boil over medium-high. Working in batches, boil pierogies until they float to surface, 2 to 3 minutes, stirring occasionally to prevent them from sticking to bottom of pot. Once pierogies float, continue cooking for 1 minute. Transfer pierogies, using a slotted spoon and shaking off excess water, to a large bowl with butter; toss until butter is melted and pierogies are evenly coated.

Divide pierogies evenly among serving plates; garnish with parsley, additional feta, and reserved cooked bacon.