Melt butter and water together. Place stuffing mix in bowl. Pour water and butter over and stir. Add 2 eggs and chicken broth, stir.
In separate bowl, combine shredded chicken, mayo, and onions. Stir well.
Place ½ of stuffing mix in bottom of a 9x13 pan. Top with all of chicken mixture. Dash salt over chicken. Top with remaining stuffing mix. Beat together remaining two eggs and milk. Pour over mixture in pan. Cover and place in refrigerator for at least eight hours.
Before baking, remove cover and spread cream of mushroom soup over top. Place in 350 oven, uncovered, and bake for 45 minutes. Remove from oven and top with shredded cheese. Return for another five minutes, or until cheese is melted.