Step 1

Preheat oven to 350°F. Lightly coat a 9-by-13-inch baking dish with cooking spray.

Step 2

Heat 1 tablespoon oil in a large saucepan over medium heat. Add ground beef and onion; cook, stirring, until the beef is no longer pink, about 5 minutes. Add garlic and cook until fragrant, about 1 minute. Stir in broth, tomato sauce, rice, 1/4 teaspoon salt and 1/4 teaspoon pepper; bring to a simmer. Cover, reduce heat to maintain a simmer and cook, stirring once or twice, until the rice is tender, about 17 minutes (the mixture will be a little saucy). Uncover and remove from heat.

Step 3

Meanwhile, heat the remaining 2 tablespoons oil in a large skillet over medium heat. Add cabbage, dill, crushed red pepper and the remaining 1/4 teaspoon each salt and pepper. Cook, stirring, until the cabbage is just tender, 5 to 7 minutes. Remove from heat.

Step 4

Spread half the cabbage in the bottom of the prepared baking dish. Top with half the beef mixture then half the cheese. Repeat with the remaining cabbage, beef mixture and cheese. Bake until hot and the cheese has melted and started to brown, about 25 minutes.