Combine warm water, warm milk, and sugar in a large bowl. Sprinkle yeast on top and rest 5-10 minutes until foamy.
Stir in melted butter, egg, and salt. Add flour gradually, mix to form dough, then knead until smooth. Cover and rise 60-90 minutes until doubled.
Cook ground beef and onion in a skillet until browned. Drain excess grease if needed.
Add cabbage, garlic, salt, pepper, Worcestershire sauce, and beef broth. Cover and cook until cabbage is tender. Cool 10-15 minutes.
Preheat oven to 375°F. Divide dough into 8 pieces and roll each into a 6×8 inch oval/rectangle.
Add filling (and cheese if using), fold dough over, pinch seams tightly, tuck ends under, and place seam-side down on a parchment-lined baking sheet.
Brush tops with melted butter and bake 18-22 minutes until golden. Rest 5 minutes before serving.