Melt butter in a large skillet over medium heat. Add chopped bacon and onions; cook and stir until the bacon is crisp and the onions are browned, 6 to 8 minutes. Remove bacon and onions to a small dish, reserving about 2 tablespoons of the bacon fat for frying the pierogi.

Place potatoes into a large pot and cover with salted water; bring to a boil. Reduce heat to medium-low and simmer until tender, about 20 minutes. Drain and mash until smooth. Allow to cool for 10 minutes. Season with salt, black pepper, and cayenne pepper. Stir in 1 egg and farmer's cheese. Cover and refrigerate until chilled, about 30 minutes.

Beat 1 egg with 1 tablespoon water in a bowl for the egg wash.

Place 2 to 3 wonton wrappers at a time on a lightly floured work surface. Brush the edges lightly with the egg wash. Place about 2 tablespoons of filling in the center of each wrapper. Fold each pierogi in half and lightly press the edges together to seal.

Bring a pot of salted water to a boil and cook pierogi in the boiling water until they float, 2 to 3 minutes. Drain.

Transfer pierogi to the skillet with reserved bacon drippings in batches and cook over medium heat until lightly browned, about 2 minutes per side. Transfer to a bowl, toss with the bacon and onions, and serve garnished with sour cream and chives.