for filling: In a large skillet, brown ground beef, seasoning with salt and pepper.
When beef is browned, remove from skillet to large bowl.
Drain extra grease from skillet.
Add butter to melt and then add cabbage, mushrooms, onion, and garlic.
Season with salt and pepper, about ½ teaspoon salt and ¼ teaspoon black pepper.
Cook over medium-high heat until cabbage is cooked through.
Remove from skillet into bowl with ground beef. Stir well.
Cover and cool in refrigerator while you make the bread.
for bread: In a mixing bowl, dissolve yeast in warm water.
Add oil and sugar; let stand for 5 minutes.
Add the egg, salt, and enough flour to form a soft dough.
Turn onto a floured surface; knead 3-5 minutes. Do not let rise.
Divide into 12 pieces; shape each into a ball.
Flatten each ball into about a 3 to 4 inch circle; add 2 heaping tablespoons of filling to center and fold dough around to completely cover filling.
Pinch edges to seal and flatten to a hamburger bun-like shape.
Place on a greased or lined baking sheet.
Repeat with remaining dough and filling, placing about 3 inches apart.
Cover and let rest for 10 minutes, meanwhile preheat oven to 425 degrees.
Bake for 8 to 12 minutes or until golden brown.
While rolls are still warm brush with melted butter.
Remove from pans to wire racks to cool.