Melt the Herb Butter in a medium skillet over medium heat. Add the onions and celery and saute until translucent, stirring occasionally, 10 to 15 minutes. Remove from heat and let cool.
Preheat the oven to 375 degrees F.
In a large bowl, combine the cooked onions and celery with the cornbread, chicken broth, milk, egg, salt and pepper. Mix well to combine. Refrigerate until ready to bake.
Transfer the stuffing mixture to a greased 9-by-13-inch baking dish. Bake until golden brown, 35 to 40 minutes.
Combine the butter, sage, parsley, thyme, rosemary, salt and pepper in a small mixing bowl. Mix to blend.