Preheat oven to 375°. Sauté first 5 ingredients in hot oil in a large skillet over medium heat 15 to 20 minutes or until tender and lightly browned. Stir in oysters and next 9 ingredients; cook 3 to 4 minutes or until edges of oysters begin to curl. Remove from heat; let stand 10 minutes. Remove bay leaves.
Place mixture in a large bowl; stir in eggs and cheese. Fold in cornbread. Place mixture in a lightly greased 3-qt. or 13- x 9-inch baking dish.
Bake at 375° for 40 to 45 minutes or until lightly browned. Garnish, if desired.
Note: To make ahead, prepare recipe as directed through Step Cover tightly, and freeze up to one month. Thaw in refrigerator 24 hours. Let stand at room temperature 30 minutes. Proceed with recipe as directed.