Cut the bread into 1/2-inch cubes. Spread the bread out on a sheet pan and let it dry overnight - OR - place the baking sheet in a 350°F oven and bake about 20 minutes, or until the bread is dried out. Set aside.
Preheat oven to 375°F. Spray a large baking dish with oil.
In a large skillet, melt the butter over medium heat. Add the onion and celery and sauté, stirring occasionally, until tender and translucent, about 8 minutes. Transfer to a large bowl.
In the same pan over medium heat, cook the sausage, crumbling with a wooden spoon, until lightly browned and cooked through, about 10 minutes. Transfer the sausage to the bowl with the onion/celery mixture.
Add the bread, sage and thyme to the bowl with the sausage/onion mixture and stir to combine. Add the chicken broth and stir to evenly coat the bread. Adjust salt and pepper to taste and stir to mix well.
Transfer to the baking dish and bake for 30 minutes. Using a wooden spoon, gently stir. Continue baking until golden, about 30 to 35 minutes more. Serve immediately.