Melt 2 Tbsp. butter with oil in a large skillet over medium heat; add mushrooms, celery, and bell pepper, and sauté 8 to 10 minutes or until vegetables are tender.
Crumble cornbread into a large mixing bowl. Stir in mushroom mixture, half-and-half, and next 6 ingredients, and, if desired, rosemary. Add chicken broth, and gently stir until moistened. Spoon into a lightly greased 13- x 9-inch baking dish.
Bake, covered, at 350° for 25 to 30 minutes or until golden.