Heat the oven to 375°F and grease a 9-by-13-inch baking dish.
Brown the sausage in a large skillet over medium-high heat for 7 to 9 minutes, breaking it into crumbles, then transfer it to a large bowl.
Cook the apple, onion and celery in the sausage drippings for 6 minutes, until the onion softens, and add them to the bowl.
Add the bread, sage, thyme, salt and pepper and toss until evenly mixed.
Whisk the eggs, broth and melted butter together, pour over the bread mixture and fold until every cube is moistened.
Spread the mixture in the dish, cover with foil and bake for 25 minutes.
Uncover and bake for 15 to 20 minutes more, until the top is crisp and the center reaches 160°F.
Rest for 10 minutes before scooping.