Bring a large pot of water to a boil. Add cabbage leaves and cook just until tender, about 3-5 minutes. Drain and rinse immediately with cold water.
In a bowl, combine ground beef, rice, diced zucchini, carrots and onions, 1 t. salt, 1/2 t. pepper, 1/2 t. garlic powder and 1/4 t. allspice.
To assemble the rolls, cut out a triangular section of any remaining tough stem. Using your hands, form a log with some of the meat mixture. Place in the center of the cabbage leaf and roll up burrito style, tucking the sides in first then rolling the rest. Repeat until done.
In a small bowl, whisk together the remaining ingredients. Pour 1/2 the sauce into the bottom of a baking dish. Place the cabbage rolls on top and cover with remaining sauce.
Cover dish with aluminum foil and bake at 375 degrees for 30 minutes. Remove foil and bake an additional 10-15 minutes, until sauce thickens and meat is fully cooked.