Cut off pointed ends of garlic bulbs; place garlic on a piece of aluminum foil, and drizzle with olive oil. Fold foil to seal.
Bake at 350° for 45 minutes; cool. Squeeze pulp from garlic cloves into a large bowl. Add rice and cornbread.
Cook sausage in a large skillet over medium heat, stirring until it crumbles and is no longer pink; drain sausage on paper towels, and wipe skillet clean.
Melt butter in a skillet over medium-high heat. Add onion, bell pepper, and carrot, and sauté 3 minutes or until tender.
Stir sausage, vegetables, parsley, and next 4 ingredients into rice mixture. Add broth; stir to moisten. Spoon into a lightly greased 13- x 9-inch baking dish. Cover and chill 8 hours, if desired; remove from refrigerator, and let stand at room temperature 30 minutes.
Bake, covered, at 350° for 45 minutes or until thoroughly heated.