1. Heat oil in a sauté pan. Add diced onions and cook, stirring occasionally, for five to six minutes or until the onions begin to brown. Add minced garlic and cook for two minutes. Pour the onion-and-garlic mixture into the slow cooker.
2. In the same pan you used to sauté the onions, break up the beef. Season with salt and pepper and cook until browned.
3. Chop up rinsed cabbage leaves and set aside.
4. When the beef is browned, begin to layer: Start by placing half of the cabbage in the slow cooker and top with half of the beef. Pour diced tomatoes on top. Repeat with remaining cabbage and beef. Add tomato soup, then fill up one of the cans with water and add to the slow cooker. Season with a little more salt and pepper.
5. Cook on high for four hours or low for six to eight hours.
6. Serve with white rice.