Combine the flour, salt, melted butter, Greek yogurt, and egg in a mixing bowl. Mix everything together until it forms a smooth dough. Knead the dough lightly for a couple of minutes, then cover it with a kitchen towel or plastic wrap to rest for 30 minutes. This resting period makes the dough soft and easy to handle later.
While the dough rests, boil the peeled and quartered potatoes in salted water until soft, about 30 minutes. Drain well, then mash the potatoes with butter, shredded sharp cheddar cheese, and cream cheese. Season with salt and pepper to taste. You’ll end up with a creamy, cheesy filling that’s irresistible even on its own!
On a well-floured surface, roll out your dough to about 1/8-inch thickness. Use a biscuit cutter or the rim of a drinking glass to cut out 3-inch rounds. Spoon about 2 teaspoons of the potato filling into the center of each circle. Lightly brush the edges with water, fold into half-moons, and pinch or crimp the edges to seal them tight.
Bring a large pot of salted water to a gentle boil, then drop in the pierogies in small batches. Cook for 2-3 minutes or until they float to the surface. Use a slotted spoon to remove them and set aside.
Cook the chopped bacon in a skillet until crispy, then transfer to a paper towel-lined plate. Retain about a tablespoon of the rendered bacon fat and add the butter to the skillet. Sauté the sliced onions over medium-low heat until they caramelize beautifully, which may take about 20 minutes. Deglaze the pan with apple cider vinegar for extra depth, then add thyme for a fragrant touch.
Gently toss the boiled pierogies into the skillet with the onions until they’re coated in the buttery, caramelized mixture. Plate them up, then top with crispy bacon bits, fresh thyme, and an extra sprinkle of cheddar if you like!