In a medium-sized pot, add the peeled and cubed potatoes and 1/4 cup of diced onion. Fill the pot with water until it is about 1-2 inches above the potatoes. Boil the potatoes on high, then let them simmer for about 20 minutes.
Make the mashed potato filling
Drain the water and add the butter, sour cream, salt, pepper, and garlic powder for the filling. Beat with an electric hand mixer on high until smooth and creamy.
Once the mixture is completely cooled, add the shredded cheese and mix. Set aside.
In a stand mixer, sift in the flour and salt. Then add the warm milk, eggs, melted butter, and sour cream to a large measuring cup and whisk to combine. Pour it into the stand mixer bowl with the flour.
Make the pierogi dough
With the hook attachment, begin mixing on a low speed and increase to high. Mix the dough for about 10 minutes, until it becomes smooth and elastic. If needed, you can add a little more flour, only a tablespoon at a time though.
Now transfer the dough to a lightly greased bowl and cover it with plastic wrap. Let it rest for at least 30 minutes.
Place the dough on a floured surface and divide it into quarters and round each one into a ball. Roll each ball out to about 1/16th of an inch thick, so very thin. Keep the rest of the dough covered so it doesn’t dry out.
Using a 3-inch biscuit cutter or glass cup, cut out as many circles as you can. Cover the scraps with plastic wrap to keep moist.
Place 1/2 tablespoon of potato filling into each piece of dough, lightly press the filling to get out air pockets, and then fold the dough into a half-moon shape. Pinch the ends together and make sure the seal is tight. You could also crimp the edges for a prettier appearance.
Repeat the filling process with the rest of the dough. Then reshape the scraps of dough to roll out, cut, fill, and seal. Repeat this with all the dough until it’s gone, which should come to about 60 pierogi.
Make the caramelized onions. Dice the onion and then add it to a skillet with unsalted butter over medium heat. Stir until the onion is caramelized and translucent.
Boil the pierogi. Salt a pot of boiling water and carefully add the pierogi, one at a time. Boil them for 3-5 minutes after they float to the top. Transfer them with a slotted spoon to a bowl or plate and top with caramelized onions. Serve with a dollop of sour cream.