To make the dough, in a large bowl, whisk together the eggs, milk, sour cream and salt. Add 3 cups flour and stir with a wooden spoon, adding as much of the remaining flour as needed to form a shaggy dough. Knead with your hands in the bowl until dough starts to stick together. Transfer to a lightly floured work surface and knead by hand until soft and smooth, about 3 minutes. Cover with plastic wrap and let rest at room temperature for at least 2 hours.
To make the filling, heat a large skillet over medium-high heat with the oil. Once hot, add the ground sirloin and cook, crumbling with a wooden spoon, until crispy and browned, about 5 to 8 minutes. Stir in the onions, season with salt, pepper, red pepper flakes, and Worcestershire sauce and cook for a minute or two longer. Remove from heat and let cool.
In a separate skillet, cook the bacon until crispy. Transfer to a plate lined with paper towels, using a slotted spoon. In the same skillet add the sliced onions (for the topping) and cook on medium, until soft, translucent and caramelized, about 10 minutes. Season with salt and pepper. Remove from heat and set aside.
Stir the crispy bacon and pickles into the ground beef mixture.
Meanwhile make the sauce, in a small bowl, stir together the sour cream, mayo, ketchup, mustard, hot sauce and pickles until well combined. Cover with plastic wrap and chill until ready to serve.
Once the dough is ready, cut into quarters. Working with one portion at a time, keeping the others covered with plastic wrap, roll out on a well floured work surface about a 1/8 of an inch thick. You want it very thin. Make sure to continuously lift the dough from the board and dust with flour as needed. Cut into rounds with a 4 inch cutter, reserve scraps for later. Fill with a tablespoon of meat filling and a sprinkling of cheddar cheese. Fold over into half moon shape, seal with egg wash and secure with a fork. Place the pierogi on a baking sheet dusted with cornstarch and continue filling the rest. Repeat with the other portions of dough, rolling out, cutting, filling and sealing. Once all pierogi are filled cover the baking sheet loosely with plastic wrap.
Fill a large pot with cold water and bring to a boil. Season with salt and slowly drop in a few pierogi at a time. Cook until soft, wrinkled and floating, about 2 minutes. Transfer to baking sheet lined with parchment paper, with a slotted spoon, and continue cooking the remaining pierogi.
In a large skillet, set over medium heat, melt and brown the butter. Add the pierogi, half at a time, and cook until golden brown and crispy on both sides, about 3 minutes. Transfer to a plate and cook the remaining pierogi.
Serve warm with the caramelized onions and the burger sauce we made earlier. Enjoy!