To Make Meat Mixture: Heat 2 tablespoons oil in a large skillet over medium high heat. Saute onions until golden brown, then remove from skillet and set aside. Add remaining 2 tablespoons oil to skillet and heat for 1 minute over medium high heat. Add beef and cook until browned, mashing with a fork to break into small pieces. Drain fat.
Place beef, sauteed onions, salt and pepper in a blender and blend on high for 5 to 7 seconds; set aside.
To Make Dough: In a medium bowl, combine flour, salt and egg and mix well. Stir in water, a little bit at a time, until dough is stiff. Knead dough for 2 to 4 minutes on a lightly floured surface. Roll out dough to 1/8 inch thickness with a rolling pin. With a glass or cookie cutter, cut out rounds about 3 inches in diameter.
Preheat oven to 400 degrees F (200 degrees C).
Place 1 tablespoon filling on 1/2 of each dough circle. Moisten edges of dough with a little water; fold dough over filling and press edges together, first with your fingers, then with a fork.
Place piroshki on a lightly greased cookie sheet and bake for 30 minutes, or until golden brown. Brush with melted butter and serve at room temperature.
