1. To prepare the gravy, melt 1/2 cup of butter in a saucepan over medium-high heat. Add the sausage and cook until browned and crumbled, about 5-7 minutes. Stir in the flour to create a roux and let it cook for 2 minutes, stirring constantly. Gradually pour in the milk, whisking continuously until the mixture comes to a boil and thickens. Season with cayenne pepper, salt, and black pepper to taste. Allow the gravy to cool to room temperature, then refrigerate for at least 2 hours until thick and chilled.

2. Preheat your oven to 400°F and grease a 12-cup muffin tin. Melt 4 tablespoon of butter in a pan over medium heat, then add the onion, celery, poultry seasoning, salt, and pepper. Cook until the vegetables are translucent, about 4-5 minutes.

3. Pour the hot broth over the bread cubes, parsley, sage, and thyme in a large bowl, and mix well. Stir in the beaten eggs until fully combined.

4. Scoop the stuffing mixture into the prepared muffin cup, pressing down slightly. Use your finger to create a hole in the center of each muffin, leaving about 1 inch from the bottom. Spoon 2 tablespoon of the chilled gravy into each hole, then cover with additional stuffing.

5. Brush the tops of the muffins with the remaining melted butter.

6. Bake for 20 minutes until golden brown and firm. Allow to cool in the pan for 5-10 minutes before serving.