Preheat oven to 350F. Cube the bread, spread on a baking sheet and bake until lightly toasted, 15 to 20 minutes.
Cook sausage in a large nonstick skillet over medium heat, stirring with a wooden spoon to break it up, until no longer pink, 5 to 10 minutes. Drain in a colander to remove excess fat.
Add oil to the pan and heat over medium-low heat. Add celery, onions and garlic; cook, stirring, until softened, about 5 minutes. Peel and chop the apples. Add apples to the pan and cook, stirring, until tender, 8 to 10 minutes more. Transfer to a large bowl.
Add the sausage, toasted bread, sage, thyme and basil to the bowl. Toss well. Drizzle broth over the mixture and toss until evenly moistened. Season with salt and pepper. Transfer to a lightly oiled 9-by-13-inch baking pan.
Cover the stuffing with foil and bake until heated through, 35 to 45 minutes. If you want a crisp top, uncover it for the last 15 minutes.