Preheat the oven to 325 degrees F. Butter a shallow 3-quart baking dish. Cut or tear the bread into bite-size pieces. Divide between 2 rimmed baking sheets and spread into a single layer. Bake until slightly dry and crisp, 15 to 20 minutes. Cool completely.
Meanwhile, cook the sausage in a large nonstick skillet over medium-high heat, breaking up the meat into small pieces with a wooden spoon until browned and cooked through, about 5 minutes Transfer the sausage to a plate using a slotted spoon. Add the cranberries, thyme, apple, onion, celery, 1/2 teaspoon salt and a few grinds of pepper to the drippings in the skillet and cook, stirring occasionally, until soft, about 5 minutes. Add the broth and parsley and bring to a boil. Remove from the heat and pour into a large bowl.
Add the toasted bread to the onion mixture and toss until evenly moistened. Stir in the egg and cooked sausage. Transfer to the prepared baking dish and evenly spread without packing the stuffing down too much. Bake until the top is crusty, about 40 minutes. Drizzle the melted butter over the top and continue to bake until the top is crisp and golden, about 20 minutes more. Sprinkle the top with some chopped parsley.
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