If you have a food processor, shred your cabbage, onion, and cheese. If you prefer, the cabbage and onion can be finely diced.
Place ground beef, garlic, and onion in a large skillet and cook over medium heat. Stir frequently and break up the beef into crumbles.
When most of the beef is cooked (a small amount of pink is okay), drain excess beef grease if needed. A teaspoon or two of oil in the pan is okay. Add cabbage and seasonings to the pan and stir. Cover and reduce to low heat. Simmer for 30 minutes.
Cool at least 15 minutes. The filling can be made in advance and stored in the refrigerator until ready to assemble.
Preheat oven to 350 degrees.
Divide bread dough into 10 equal balls (about 3 ounces each). On a floured surface, roll out each ball until it is ¼-inch thick. If it bounces back thicker, continue rolling until it stays the desired thickness.
Place ⅓ cup of filling in the center of each piece of flattened dough. Top with 2 tablespoons shredded cheese.
Pull the dough around the filling, pinching into a rectangle. Be sure the dough is pinched tightly.
Place each filled rectangle pinched side down into two large baking dishes, with each rectangle spaced at least 2-inches apart.
Let the dough rise at room temperature for 30 minutes.
Place the baking dishes in the oven and bake at 350 degrees for 20 minutes. Brush with melted butter and bake an additional 5-10 minutes, or until golden brown. It should sound hollow when tapped.