Preheat the oven to 350 degrees . In a large skillet, melt the butter over medium heat, then add the sausage and cook for 5 minutes, crumbling the meat with the back of a spoon. Add the celery and onion and cook until the vegetables are tender and the meat is browned, 7 to 10 minutes. Transfer the mixture to a large bowl and let cool.
Add the bread cubes, crackers, thyme, eggs, stock and parsley to the bowl and mix well (use your hands if you like-its fun). The mixture should be moist but not soggy; add a little more stock if you like your stuffing wetter. Season the stuffing with salt and pepper. Place in a 9-by-13-inch buttered baking dish and bake for 1 hour. (To keep the stuffing moist, cover the top loosely with foil while it bakes.)