Combine 1 cup whole milk, 1 teaspoon salt, 1 large egg, and ½ cup water in a stand mixer. Gradually add 3 cups all-purpose flour until the dough comes together. Knead briefly for about 5 minutes. Cover and let rest for 15-30 minutes.

Mix together ½ pound ground pork, ½ pound ground chicken, 1 finely chopped medium onion, and 2 minced garlic cloves. Season with salt, black pepper, and 1 tablespoon vinegar. Stir and let sit for about 10 minutes.

Roll out the dough to 1/8 inch thickness. Cut out circles and place a spoonful of filling in each. Top with another layer of dough and roll the mold to seal edges.

For hand shaping, roll into thin sheets, cut into squares, place filling in each, fold to create triangles, and pinch edges firmly to seal.

In a pot of boiling salted water, cook pelmeni in batches for 2-3 minutes until they float. Remove with a slotted spoon and serve.

Serve the pelmeni warm with melted butter and fresh dill; offer sour cream or vinegar on the side.