Prepare the Dough: Make or use pre-prepared pierogi dough, cover, and let it rest for 30 minutes at room temperature.
Cook the Aromatics: Heat olive oil in a skillet over medium heat. Sauté the diced onion for 5 minutes until softened and golden, then stir in minced garlic for 1 minute until fragrant.
Prepare the Filling: In a mixing bowl, combine the cooked onion mixture with ground meat, salt, pepper, and water. Mash until just combined—avoid overmixing to keep the meat tender.
Roll and Cut Dough: Halve the dough, wrapping one piece in plastic wrap. Roll the other half on a floured surface until it’s less than ⅛ inch thick. Use a 2½-inch cookie cutter to cut out as many circles as possible, reusing scraps as needed. Repeat with the remaining dough.
Fill and Shape Dumplings: Place 1 teaspoon of meat filling in the center of each dough circle. Fold the dough over, pinching the edges tightly, and shape into a crescent or ear shape. Arrange pelmeni on parchment-lined baking sheets.
Cook the Pelmeni: Bring a large pot of salted water to a boil. Add half of the pelmeni and stir to prevent sticking. Boil until they float, about 6 minutes. Reduce heat and simmer another 3 minutes until the meat is cooked. Use a skimmer to transfer pelmeni to a serving bowl.
Serve: Drizzle melted butter over the cooked pelmeni and garnish with dill, if desired. Serve with sour cream, vinegar, or ketchup for dipping.