Add canned diced tomatoes, tomato sauce, broth, dry rice and the seasoning to your slow cooker.
Brown the ground beef in a skillet, and transfer it to the slow cooker. Leave some of the grease from the meat behind in the skillet.
Add diced onions to the pan you used to cook the meat, and sauté these for a few minutes until they are soft and translucent. Then, add finely grated garlic to the skillet, and sauté for another minute. Transfer the onion and garlic to the slow cooker.
Lastly, peel and dice the carrots, and roughly chop or slice the cabbage. Add these to the slow cooker, and stir to combine the ingredients.
Cover with a lid, and cook the cabbage roll soup on high for 4-6 hours, or on low for 7-8 hours. Taste the soup to check if it requires any additional seasoning, and to make sure that the rice has cooked through before serving.