Soak mesquite chips in water at least 30 minutes; drain.
Peel outer skins from garlic; cut off and discard top one-third of garlic head. Place garlic (cut side up), tomato halves (cut side down), and next 3 ingredients in a grill basket.
Pile charcoal on each side of grill, leaving center empty. Place a drip pan between coals. Prepare fire; let burn 10 to 15 minutes. Place half of mesquite chips on hot coals. Coat grill rack with cooking spray, and place over coals. Place grill basket on rack over drip pan; cover and cook 30 minutes. Turn vegetables, and add remaining mesquite chips to hot coals. Cover and cook 30 minutes or until vegetables are tender and lightly browned.
Remove vegetables from grill. Squeeze out pulp from each clove of garlic. Position knife blade in food processor bowl; add garlic pulp, vegetables, tomato sauce, and remaining ingredients. Process until smooth, scraping sides of processor bowl twice. Serve with meat loaf, turkey burgers, turkey franks, and sloppy joes.