1. Start by melting the butter in a saucepan over medium-high heat. Add the sausage and cook, breaking it up with a wooden spoon, until it’s browned and crumbled, about 5-7 minutes. Stir in the all-purpose flour to create a roux, and let it cook for an additional 2 minutes, stirring constantly.

2. Gradually whisk in the milk. Continue stirring until the mixture comes to a boil and thickens, creating a rich, velvety gravy. Season with the cayenne pepper, salt, and black pepper to taste. Once the gravy has reached the desired consistency, remove it from the heat and let it cool to room temperature. Then, transfer it to the refrigerator and chill for at least 2 hours, or until it’s thick and chilled.

3. Preheat your oven to 400°F and grease a 12-cup muffin tin with butter.

4. In a pan, melt 4 tablespoon of butter over medium heat. Add the chopped onion, celery, poultry seasoning, salt, and pepper. Sauté the vegetables until they’re translucent, about 4-5 minutes. Now, pour in the chicken or turkey broth and bring the mixture to a boil.

5. In a large bowl, combine the bread cubes, chopped parsley, sage, and thyme. Pour the hot broth mixture over the bread mixture and stir well to ensure the bread is evenly coated. Finally, gently stir in the lightly beaten eggs until everything is fully incorporated.

6. Scoop the stuffing mixture into the prepared muffin cup, pressing down slightly to compact it. Using your finger, create a hole in the center of each muffin, leaving about 1 inch from the bottom. Carefully spoon 2 tablespoon of the chilled gravy into each hole, then mold additional stuffing over the top to cover the gravy.

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

8. Place the muffin tin on the middle rack of your preheated oven and bake for 20 minutes, or until the tops are golden brown and the muffins are firm to the touch.

9. Allow the muffins to cool in the pan for 5-10 minutes before serving.