In a large heavy pot, melt the butter over medium-high heat. Add the chopped onion and celery and saute until very tender. Season to taste with salt and pepper. The vegetables will break down and start to brown a bit. This process may take up to 15 minutes or longer.
Empty the bags of stuffing mix into a large mixing bowl. Add the vegetable mixture as well as the parsley, sage, tarragon, rosemary, and thyme. Stir gently to combine. Season to taste with salt and pepper.
Add the stock, a cup at a time, until the stuffing is barely moistened.
Grease two 9x13-inch baking dishes. Preheat oven to 350 degrees.
Divide the mixture between the two pans. Bake for 45 minutes and then uncover to brown and crispen the top, according to your preferences.
Note: stuffing may be frozen prior to baking. Cover well, chill, and freeze. Thaw before proceeding with the recipe.Leftover stuffing is good, stored in the refrigerator, covered, for up to 4 days.