In a large, deep skillet over medium heat, melt the butter. Add the onion, celery, carrot, garlic, thyme, marjoram and sage. Cover and cook, stirring once or twice, until the vegetables are becoming tender, about 10 minutes. Add the mushrooms and 2 teaspoons salt, cover and cook, stirring once or twice, until the mushrooms begin to give up their juices, about 7 minutes. Uncover the skillet, raise the heat slightly and cook, stirring often, until the mushroom juices evaporate and the vegetables begin to brown, about 10 minutes. Remove the heat and cool slightly.
In a large bowl, thoroughly combine the corn bread, mushroom mixture, milk, pecans, parsley, an additional teaspoon of salt, and pepper. Spoon the dressing into the prepared baking dish. Cover and bake for 20 minutes. Uncover and bake until the top is lightly browned, 15 to 20 minutes. Let rest in the pan on a rack for 5 minutes before serving.