In a large mixing bowl, beat together one egg, sugar, and salt until well combined. Gradually add warmed milk and vegetable oil, stirring to mix. Slowly sprinkle in the sifted all-purpose flour along with the instant yeast, creating a sticky dough. Knead the dough on a lightly floured surface for about 8-10 minutes until it is smooth and elastic.

Transfer the kneaded dough into a greased bowl, covering it with a clean kitchen towel or plastic wrap. Place the bowl in a warm, draft-free area and let it rise for 60-90 minutes, or until it has doubled in size.

While the dough rises, peel and boil the potatoes in salted water until tender, roughly 15-20 minutes. Drain and mash the potatoes with unsalted butter until creamy. In a skillet over medium heat, sauté chopped onions in butter until translucent, then add ground meat, cooking until browned. Mix this with the mashed potatoes, seasoning with paprika, dill, salt, and pepper to taste.

Once the dough has risen, punch it down to release excess air and divide it into 12 equal pieces. Roll each piece into an oval shape, about 4-5 inches long. Spoon a tablespoon of the creamy potato and meat filling into the center of each oval, then fold and pinch the edges to seal tightly.

In a deep pot or heavy skillet, heat vegetable oil to 350°F-375°F. Carefully place a few piroshki in the hot oil, frying for about 5 minutes or until they are golden brown and puffy, flipping halfway through for even cooking.

Let the piroshki cool slightly before serving. Enjoy these golden Russian piroshki warm, either on their own or with a delightful dollop of sour cream on the side.