Brown the lean ground beef with the diced onion in a large skillet. Season with salt and pepper. Preheat the oven to 350 F.
Combine the chopped cabbage, rice, and tomato sauce in a large bowl. Season with salt and pepper.
Assemble the casserole: spoon half of the cabbage/rice mixture into a 9x13-inch baking dish. Sprinkle the cooked meat over the cabbage and top with the remaining chopped cabbage/rice mixture.
Pour two cups of beef broth evenly over the casserole. Add the fresh thyme and bay leaves on top, cover with foil, and bake for 1 hr and 20 mins. Halfway through the baking time, remove from the oven, mix it up, cover again and continue baking.