Cook the beef: Heat oil in a skillet over medium heat. Add ground beef and cook until browned. Drain excess fat, leaving about 2 tablespoons in the skillet. Remove beef and set aside.
1 tablespoon cooking oil, 1 pound ground beef
Sauté the veggies: In the same skillet, melt the butter. Add onions and cook for 3 minutes. Stir in garlic, carrot, and bell pepper, cooking until softened.
1 tablespoon unsalted butter, 1 clove garlic, 1 medium carrot, ½ cup red bell pepper, 1 medium onion
Add liquids: Stir in tomato paste and broth, bringing the mixture to a gentle boil.
2 tablespoons tomato paste, ½ cup vegetable broth
Cook the cabbage: Add cabbage, salt, pepper, paprika, and sugar (if using). Stir well, cover, and let simmer for 8-10 minutes, stirring occasionally.
½ of a whole green cabbage head, 1 teaspoon sugar, ⅛ teaspoon black pepper, 1 teaspoon ground paprika, ½ teaspoon salt
Combine everything: Return the cooked beef and rice to the skillet, stirring until fully combined and heated through.
1 ½ cup cooked rice
Serve: Enjoy warm, topped with fresh dill and a dollop of sour cream!
