Peel the carrots and onions. Cut each into several large pieces, then pulse in a food processor until finely diced. You don't want a puree situation on your hands - just a very fine dice.
Place the onion and carrot mixture in a large pan with the ground beef. Cook over high heat until the beef is cooked through. Remove from heat and drain the fat. Return the meat and vegetable mixture to the pan. Add the remaining ingredients and simmer over medium-low heat, uncovered, for about 30 minutes or until desired consistency.