Preheat the oven to 350°F. Butter an 8x8-inch or 1½-quart baking dish. Put the bread cubes in a large bowl.
Cook the sausage in a large skillet over medium-high heat for 5–6 minutes, breaking it up, until browned. Scoop it into the bowl with the bread, leaving the drippings in the pan.
Add the butter, onion and celery to the skillet. Cook over medium heat for 4–5 minutes, until soft. Add the apple, sage and thyme and cook for 2 minutes more.
Add the onion mixture to the bowl. Pour in 1 cup of the broth, add the salt and pepper, and toss gently. Add more broth a little at a time if any cubes are still dry.
Spread the stuffing in the baking dish and cover with foil.
Bake for 20 minutes. Uncover and bake for 10–15 minutes more, until the top is golden and crisp.