Place 20 dinner rolls 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.
Meanwhile, heat olive oil in a medium skillet and sauté onions until they become translucent. Add in the shredded carrot and cook until it begins to soften.
Add in the ground turkey breast and keep stirring until it's fully cooked. Mix in the shredded mozzarella and season with salt and pepper to taste.
Flatten each dinner roll into a disk, making sure to leave the middle a little thicker than the edges.
Fill each flattened dinner roll with 1 heaping tablespoon of the meat filling and pinch the edges of the dough together to make a half moon shape.
To ensure that the edges are pinched well, I go around a second time folding over the edge and pinching them again. Once all the piroshki are closed up, let them proof for another 30 minutes at room temperature.
Fill a heavy bottomed pot or pan with about 2 inches of corn oil and heat it over thigh heat.
Deep fry the pirushki for 2 minutes on each side or until golden brown.