Turn a slow cooker onto the highest setting and allow to preheat.
Chop onion, celery, mushrooms, and parsley.
Melt butter in slow cooker, then add the veggies and parsley (as if you're sautéing right inside the slow cooker. It should be hot enough to start softening the vegetables).
Once veggies have begun to soften, add bread cubes and sprinkle all seasonings on top.
Combine egg with chicken broth and whisk slightly. Pour over bread cubes.
Stir to combine, then turn heat down to low. Cover, and cook for 4 hours.