
Spread out the bread cubes on 2 baking sheets, loosely cover, and let dry out for 24 to 48 hours.
When you're ready to cook, preheat the oven to 375°F.
In a large Dutch oven, melt the butter over medium heat. Add the onion and celery and cook, stirring occasionally, until the onions begin to soften, about 5 minutes. Add the apples and cook, stirring occasionally, until they begin to soften, about 5 minutes more. Add the sage, thyme, and salt, and stir to combine.
Add 3 1/2 cups of broth to the Dutch oven. Bring it to a simmer and cook until the apples are just tender, 6 to 7 minutes. Remove from the heat. Add the dried cranberries, then stir in the bread cubes and toss until the bread is evenly soaked, adding the remaining 1/2 cup of broth, if needed. Stir in the parsley.
Transfer to a 13-by-9-inch baking dish. Bake, uncovered, until golden brown and crisp on top, 35 to 40 minutes. Let rest for 20 minutes before serving.