Preheat the oven to 350º. Coat a 9- x 13-inch baking dish with 2 teaspoons olive oil.
Heat remaining 1 teaspoon olive oil in a large nonstick skillet over medium-high heat. Add celery and onion; sauté 5 minutes. Add apple, parsley, sage, thyme, and rosemary; sauté 3 minutes.
Combine apple mixture, bread, and next 5 ingredients (through egg) in a large bowl. Add hot broth; stir well. (Mixture should be moist but not soaked.) Spoon into prepared baking dish. Dot with butter. Cover with foil.
Bake at 350º for 30 minutes. Uncover; bake 25 minutes or until top is golden brown. Let stand 15–20 minutes before serving.