To prepare sauce, heat a small saucepan over medium heat. Coat pan with cooking spray. Add onion and next 5 ingredients (through garlic) to pan; cook 5 minutes, stirring occasionally. Stir in broth, sugar, allspice, and tomatoes. Partially cover, reduce heat, and simmer 20 minutes, stirring occasionally.
To prepare coo-coo, place cornmeal and 1 teaspoon salt in a large saucepan. Gradually add 7 cups water, stirring constantly with a whisk. Bring to a boil. Reduce heat to medium, and cook 15 minutes, stirring frequently. Add corn and okra; cook 2 minutes or until thoroughly heated, stirring constantly. Remove from heat. Place butter in a small skillet over medium heat; cook 2 minutes or until browned. Add butter to coo-coo; stir well. Serve sauce over coo-coo.