Melt butter in a saucepan and add sugar. Beat the egg and milk together; add to butter mixture. Bring to a boil, stirring constantly. Remove from heat. Add the nuts, coconut, and graham cracker crumbs. Pour over the crackers in the pan. Cover with another layer of whole graham crackers.
Beat all the topping ingredients together and spread it over the top layer of crackers. It's stiff when you spread it. Chill. The cookies will soften to perfection. Cut into about 15 squares (or 20 in a pinch).