Melt butter in a large skillet over medium heat. Add celery, onion, mushrooms, and parsley; sauté until soft, 5 to 7 minutes.
In a large bowl, combine bread cubes and cooked vegetables. Add salt, sage, poultry seasoning, thyme, pepper, and marjoram. Toss together well. Add egg and enough broth to moisten.
Lightly pack stuffing mixture into a slow cooker. Cover and cook on High for 45 minutes. Reduce to Low and cook for 4 to 8 hours.