For the Filling: Line a fine-mesh strainer with 4 layers of cheesecloth and set in a large mixing bowl. Place cottage cheese on cheesecloth and fold over and cover with overhanging cheesecloth. Place a heavy weight, such as a 28-ounce can tomatoes, on top. Refrigerate until cheese is slightly crumbly and no moisture remains, at least 24 hours or up to 48 hours.

Using a wooden spoon or flexible spatula, press strained cottage cheese through a fine-mesh strainer set over a small bowl. In a separate small bowl, combine 300g (10 ½ ounces) of the strained cottage cheese with egg yolk and salt. Using a flexible spatula, mix until no streaks of yolk remain. Refrigerate until chilled and firm, at least 30 minutes.

For the Dough: In a medium bowl, whisk 210g flour and salt to combine. Add butter, and use your fingers to press the butter into flour until you have a crumbly mixture and butter is fully incorporated into flour, about 1 minute. Using your fingers, make a well in the center of the mixture. Add egg, sour cream, and water, and, using a fork, mix until a shaggy dough forms. Dust a clean work surface with remaining 75g flour. Gently knead dough to gradually incorporate flour, until dough is soft, smooth, and all the flour has been incorporated, about 5 minutes. Return dough to medium bowl. Cover bowl tightly with plastic wrap and rest at room temperature until dough is soft and supple, about 20 minutes.

For Shaping and Cooking: Once dough has rested, turn out onto a lightly floured work surface. Using a rolling pin, roll dough into a roughly 19-inch circle about 1/16-inch to ⅛-inch thick. Using a 3-inch cookie cutter (or a glass), punch out 25 rounds of dough. Cover dough with a clean kitchen towel and rest for 10 minutes. Meanwhile, line a rimmed baking sheet with parchment, dust lightly with flour; set aside.

To Fill the Dumplings: Place half a tablespoon (11g) of filling in the center of each dough round. Working with one dough round at a time, fold dough over the filling to form a half-moon while distributing filling to fit within it, and firmly pinch edges to seal. Transfer the cheese dumplings to prepared baking sheet. Repeat with remaining dough and filling. You should have 25 dumplings.

To Cook the Dumplings: In a 6-quart pot, bring 4 quarts (3.8 liters) of water to a boil. Salt boiling water with 2 tablespoons (about ¾ ounces; 20g) kosher salt. Carefully add half of the dumplings to boiling water, gently stirring with a spatula or wooden spoon to prevent the dumplings from sticking to the bottom of the pot, and cook until dumplings float, about 2 minutes. Once floating, cook for 1 more minute to ensure the dough and filling are heated through. Using a spider skimmer, transfer the varenyky, shaking off excess water as needed, to a large bowl with 2 tablespoons (28g) butter. Gently toss to evenly coat varenyky. Repeat with remaining dumplings.

Serve cheese varenyk with a dollop of cold sour cream and chopped dill.