Lightly grease the bottom and sides of a 6-quart slow cooker with butter.
Toss the stale French bread, butter, onions, carrots, celery, thyme and 1 teaspoon each salt and pepper in the slow cooker. Pour the chicken broth over the bread mixture and toss to coat. Use your hands to tear teaspoon-size pieces of the Italian sausage and put them directly on top of the bread mixture. The sausage should cover most of the stuffing.
Cover the slow cooker and cook on low until the sausage is cooked through and the vegetables are tender, about 4 hours. Remove the lid and gently stir the sausage into the stuffing. Season to taste with additional salt and pepper. Transfer to a shallow serving dish and garnish with the chopped parsley. Serve hot.
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For this recipe it is important the French bread is extremely stale (on the verge of dried-out). If you do not have the time to leave the bread out to become stale overnight, simply dry out the cut bread in a low oven.