Combine potatoes and 1 tablespoon salt in large saucepan and cover with water by 1 inch. Bring to boil over medium-high heat; reduce heat to medium and cook at vigorous simmer until potatoes are very tender, about 15 minutes.

Drain potatoes in colander. While still hot, combine potatoes, cheddar, butter, 1/2 teaspoon salt, and 1/2 teaspoon pepper in bowl of stand mixer. Fit mixer with paddle and mix on medium speed until potatoes are smooth and all ingredients are fully combined, about 1 minute. Chill for at least 30 minutes.

Whisk flour, baking powder, and 1/2 teaspoon salt together in clean bowl of stand mixer. Add sour cream and egg and yolk. Fit mixer with dough hook and knead on medium-high speed for 8 minutes.

Line rimmed baking sheet with parchment paper and dust with flour. Roll dough on lightly floured counter into 18-inch circle, about 1/8 inch thick. Using 3-inch biscuit cutter, cut 20 to 24 circles from dough. Place 1 tablespoon chilled filling in center of each dough round. Fold dough over filling to create half-moon shape and pinch edges firmly to seal. Transfer to prepared sheet.

Melt butter in 12-inch skillet over medium-low heat. Add onion and salt and cook until onion is caramelized, 15 to 20 minutes. Remove skillet from heat and set aside.

nutes. Using spider or slotted spoon, remove pierogi from water and transfer to skillet with caramelized onion. Return water to boil, cook remaining pierogi, and transfer to skillet with first batch.

Add 2 tablespoons cooking water to pierogi in skillet. Cook over medium-low heat, stirring gently, until onion mixture is warmed through and adhered to pierogi. Transfer to platter and serve.