Preheat oven to 400°. Crumble cornbread into bowl of a food processor. Pulse 6 to 8 times or until coarse crumbs form (about 5 cups coarse crumbs).
Spread crumbs on a 15- x 10-inch baking sheet. Bake at 400° for 15 minutes or until lightly toasted.
Sauté shallot and garlic in hot oil in a Dutch oven over medium heat 3 minutes or until tender. Stir in crumbs, broth, and next 4 ingredients; cook, stirring often, 10 minutes or until mixture thickens.