Remove the stems from the mushrooms and set the mushrooms aside. Finely chop the mushroom stems and discard of the hard ends.
In a large bowl, combine the crumbled cornbread and breadcrumbs and set aside.
Heat a large skillet over medium-high heat and cook the breakfast sausage until well-browned, breaking it apart with a wooden spoon as it cooks. Remove the sausage from the pan and add it in with the cornbread mixture.
Reduce heat to medium and melt 2 tablespoons of the butter in the pan. Add in the mushroom stems, onions, celery, garlic, sage, rosemary, and salt and pepper. Saute until the onions are translucent and softened, about 10-15 minutes. Add the onion mixture to the other stuffing ingredients.
Preheat the oven to 400 degrees F.
Pour 2 cups of chicken stock over the stuffing mixture and add in one large egg, stirring well to combine. The mixture will be very moist at this point. Spoon the mixture into the mushroom caps and place on a rimmed baking sheet. Melt the remaining 2 tablespoons of butter in the pan or in a microwave-safe bowl and drizzle it lightly over the mushrooms.
Bake until the mushrooms are cooked through and the stuffing is browned on top, about 25 minutes. At this point, you can refrigerate the mushrooms for up to 3 days before reheating to serve.