Cut any large pieces of beef into pieces that are no more than a 1/2 in. Place the beef in the bottom of a 4-6 quart crock-pot or slow cooker.
Sprinkle the Italian seasoning over the beef. Peel and chop the onion and layer it over the beef. Add the carrots [whole, with any extra lg. ones split lengthwise) and garlic. Sprinkle the rice over the rest of the ingredients. Add the broth, the water and the tomatoes with their juices. Make sure the rice is submerged in the liquid [press stray pieces down into the liquid, but do not stir].
Cover the slow-cooker and cook on low for 8 to 10 hours. Season with black pepper to taste and stir well. To serve, ladle into soup bowls.