Step 1: In a bowl, combine warm milk, sugar, and yeast. Let sit for 5 minutes until frothy.
Step 2: Add egg, salt, and softened butter to the yeast mixture. Mix well.
Step 3: Gradually add flour, mixing until a soft dough forms. Knead for 5 minutes until smooth.
Step 4: Place dough in a greased bowl, cover with a towel, and let rise for 1 hour until doubled.
Step 5: While dough rises, heat 1 tablespoon oil in a pan. Cook onion until translucent, then add ground beef and pepper. Cook until browned, then cool.
Step 6: Punch down dough and divide into 8 equal pieces. Roll each into a circle.
Step 7: Place 1-2 tablespoons of filling in the center of each circle. Fold and seal edges tightly.
Step 8: Heat 2 inches of vegetable oil in a deep pan to 350°F (175°C). Fry piroshki in batches for 3-4 minutes per side until golden brown.
Step 9: Drain on paper towels and serve warm.