Preheat oven to 350°. Brown pancetta in oil in a large frying pan over medium heat, stirring often, about 10 minutes. Add garlic, celery, and onion; sauté about 4 minutes. Add apples; stir to coat. Transfer to a large bowl. Add broth to pan; stir to scrape up browned bits. Pour into bowl.
Stir in bread, parsley, and thyme. Spoon stuffing into a greased 9- by 13-in. dish, pressing down lightly to fill pan. Bake until browned and crusty, about 45 minutes.
Make ahead: Up to 1 day ahead, prepare stuffing and chill, covered. Bake about 1 hour.