Melt butter in a skillet over medium heat. Cook and stir onion, celery, mushroom, and parsley in butter until slightly softened, 5 to 8 minutes.
Place bread cubes in a very large mixing bowl. Spoon cooked vegetables over bread cubes. Season with salt, sage, poultry seasoning, thyme, marjoram, and pepper. Pour in enough broth to moisten, then mix in eggs. Transfer mixture to a slow cooker.
Cover and cook on High for 45 minutes, then reduce heat to Low and cook for 4 to 8 hours.