Vareniki (Ukrainian Pierogi Dumplings)

Make the dough Bring water and butter to a simmer in a small saucepan over medium. Meanwhile, stir together flour and salt in a large bowl; make a well in center, and add egg. While stirring constantly with a fork, slowly pour hot water mixture into well, incorporating flour mixture into egg mixture until shaggy pieces of dough form.

Transfer mixture to a lightly floured work surface along with any remaining flour in bowl. Knead, pressing any loose flour into dough, until smooth and soft, 3 to 5 minutes. If dough is too sticky, lightly sprinkle with additional flour. (Do not overwork dough.) Shape dough into a ball, and cover using plastic wrap; let rest at room temperature for at least 30 minutes or up to 1 hour.

Meanwhile, make the filling Place cottage cheese in a fine mesh strainer placed over a medium bowl, and let drain until ready to use; discard drained liquid. Place potato in a large pot and sprinkle with 1 tablespoon salt. Add enough water to cover by 1 inch. Bring to a boil over high; reduce heat to medium, and gently boil, uncovered and undisturbed, until potato is tender, about 8 minutes. Drain well; transfer to a medium bowl. Reserve the pot.

While potato cooks, melt 2 tablespoons butter in a medium skillet over medium. Add onion, pepper, and 1/2 teaspoon salt; cook, stirring often, until softened and lightly browned, 10 to 12 minutes. Remove from heat.

Using a potato masher, mash hot potato until smooth. Stir in drained cottage cheese, sautéed onion, and remaining 1/4 teaspoon salt. Refrigerate, uncovered, until cooled, about 20 minutes.

Fill the large pot with generously salted water and bring to a boil over high. While water comes to a boil, transfer dough to a lightly floured work surface. Roll into a 1/16- to 1/8-inch-thick round (about 16 inches in diameter). Using a 3 1/2-inch-round cookie cutter, cut dough into rounds; reroll dough scraps once (20 to 22 rounds total). Working with 1 dough round at a time, place 1 rounded tablespoon filling in center. Moisten dough edges with water. Fold round in half to form a half-moon that pockets the filling; press edges together firmly to seal, pressing out any air, and pleating as desired. Place on a large baking sheet lined using parchment paper; cover using a clean kitchen towel. Repeat process with remaining dough rounds and filling.

Add half of dumplings to boiling water, and gently stir once. Cook, undisturbed, until dumplings float, 2 to 3 minutes; continue cooking for 1 minute. Using a slotted spoon, transfer dumplings to a large heatproof bowl with remaining 2 tablespoons butter; toss until coated in melted butter. Repeat cooking process with remaining dumplings. Divide dumplings evenly among 4 bowls, garnish with parsley, and serve immediately with sour cream, if desired.