Combine cottage cheese, egg yolks, and 3/4 teaspoon salt in a medium bowl; set aside.

Whisk flour, remaining 1 teaspoon salt, and baking powder together in a separate bowl. Add cold water and oil; mix or knead into a smooth dough.

Roll dough out on a lightly floured surface; cut into 3-inch circles using a glass, can, or cookie cutter. Place a spoonful of cottage cheese filling onto each circle. Fold in half and pinch edges together to seal.

Bring a large pot of lightly salted water to a boil. Carefully drop pierogies into water; cook until they float, 3 to 4 minutes. Remove from water with a slotted spoon; place on a cooling rack set over a baking sheet to drain.