Preheat an oven to 375°F. Butter a 3-quart baking dish.
In a large fry pan over medium heat, melt the butter. Add the onion, celery, sage, salt and pepper and sauté, stirring occasionally, until soft and translucent, 10 to 12 minutes. Transfer the onion mixture to a very large bowl.
In the same pan over medium-high heat, cook the sausage, breaking it into large chunks, until browned and cooked through, 8 to 10 minutes. Transfer to the bowl with the onion mixture, add the stuffing and parsley, and stir until well combined.
In a small saucepan over medium heat, whisk the garlic into the broth until combined. Stir the broth mixture into the stuffing 1/2 cup at a time, making sure it is completely absorbed into the croutons and does not pool in the bottom of the bowl. Taste a crouton; it should be moist throughout but not crunchy or mushy. You may not need all of the broth.
Transfer the stuffing to the prepared baking dish. Cover the dish with aluminum foil and bake for 20 minutes. Remove the foil and continue baking until the top is golden brown, 25 to 30 minutes more. Let rest for 10 minutes before serving. Serves 10 to 12
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