Brown the beef and onion in a skillet over medium-high heat for 8 to 10 minutes until the beef reaches 160°F, then drain the fat.
Stir in the garlic for 30 seconds and transfer the mixture to a 6-quart crockpot.
Add the cabbage, crushed tomatoes, tomato sauce, broth, Worcestershire, paprika, salt and pepper.
Cover and cook on low for 6 hours until the cabbage is tender but still visible in ribbons.
Add 3/8 cup cooked rice to each bowl before ladling in the soup; freeze any leftover soup without rice.