Cook rice with a rice cooker or stovetop, following package instructions.
1 cup rice
If you like your cabbage well cooked, add the cabbage as soon as you turn on the heat or at the beginning or the rice cooker cycle. If you want it a little more al dente, add it after the rice boils and you turn it down to simmer or about 15 minutes into the rice cooker cycle. Simply pile the cabbage atop the rice without stirring anything so that it steams.
While the rice is cooking, start on the filling. Brown your ground beef with the pepper, breaking the meat into crumbles, until no longer pink. Drain it thoroughly and place in a medium casserole dish, but save about 1 tablespoon of the grease to cook the onion in. Add the onion and cook on medium high to get some sweetness and caramelization happening.
Once the onion is translucent, add the garlic. As the onion gains a little color, add the brown sugar and stir well. After a couple minutes to allow the sugar to melt and add some more flavor, add the crushed tomatoes or prepared tomato sauce, the can of tomato sauce, and the vinegar. Stir well and let it simmer for about 10 minutes.
3 cloves garlic, 1 tablespoon brown sugar, 4 cups crushed tomatoes, 14 ounces can tomato sauce, 1 1/2 tablespoon vinegar
When the rice is done, you can see that the cabbage is also steamed and has lost some volume. Using tongs, remove the cabbage leaves and set them aside.
Preheat your oven to 350 degrees.
Add the rice to the ground beef and stir well. Once the tomato sauce has simmered, spoon just enough into the ground beef mixture to get it wet enough that it sticks together a bit.
Place the cabbage leaves atop the ground beef mixture, forming a thick layer. Spoon the remainder of the tomato sauce atop the cabbage, being sure to cover all the leaves so they don't burn.
Bake the casserole for 15 minutes in your oven, then serve immediately.