Proof the dough. Place the dough on a lightly floured cookie sheet and cover with plastic wrap. Let the dough thaw and proof for at least 1 hour at room temperature.
Add the rest of the ingredients. Now add the ground meat and keep stirring until it’s fully cooked. Mix in the shredded mozzarella cheese and season with salt and pepper to taste.
Fill the dough. Flatten each dinner roll into a disk. Then fill each one with 1 heaping tablespoon of the meat filling and pinch the edges of the dough together to make a half-moon shape.
Proof the piroshki. Once all the piroshki are closed up, place them seam-side down on a baking sheet lined with parchment paper. Let them proof for another 30 minutes at room temperature.
Fry them. Fill a heavy-bottomed pot or pan with about 2 inches of oil and heat it over high heat (350 degrees Fahrenheit). Deep fry the piroshki for 2 minutes on each side, or until golden brown. Place them on a paper towel-lined plate to blot up excess oil. Then serve them warm.