Cook rice in water or broth until tender, 15 minutes for white rice or about 40 minutes for brown rice; cool slightly.
While rice is cooking, brown ground beef (or veggie burger) and onion in a large skillet. Add tomato sauce and seasonings; cover and simmer 15 minutes. Preheat oven to 325°F; butter a 2-qt. casserole. In a large bowl, combine cooked rice with cottage cheese. Spread one-third of the rice mixture in the bottom of the prepared baking dish. Top with one-third of the meat sauce. Continue to alternate layers, ending with tomato sauce. Sprinkle with the shredded mozzarella. Bake in preheated oven about 30 minutes, or until hot and bubbly.