In a large bowl, combine the all-purpose flour, salt, sugar, and instant yeast. Gradually stir in warm milk, warm water, vegetable oil, and one egg. Mix until a dough forms, then knead for 5-7 minutes until smooth and elastic. Cover and let it rise in a warm place for 1 hour until doubled in size.

In a skillet over medium heat, melt butter. Sauté the finely chopped onion and optional mushrooms until soft and fragrant. Add the ground beef, seasoning with salt and pepper, and cook until browned, breaking it apart as it cooks.

Once the dough has risen, roll it out on a lightly floured surface and cut it into 12 even pieces. Place a spoonful of the filling in the center of each piece, folding the dough over to enclose the filling. Pinch the edges to seal securely.

Preheat your oven to 375°F (190°C). Arrange the shaped Piroshki on a baking sheet lined with parchment paper. Beat the remaining egg and brush it over the tops. Bake in the preheated oven for 15-20 minutes until golden brown.