line bottom of a 9 inch square baking pan with parchment, leaving an overhang on two sides. Place graham crackers in bottom of pan, cutting them to fit as needed.
In small pan, heat 1/3 cup cream until it barely begins to simmer. Remove from heat. Add chopped chocolate and stir until chocolate is melted and mixture is smooth. Spread chocolate mixture evenly over graham crackers. Freeze 10 minutes.
Meanwhile, in a large bowl with electric mixer, beat egg whites until frothy. Gradually add sugar and beat until stiff, glossy peaks form. Set aside. In another large bowl with electric mixer, no need to clean beaters, beat cream of coconut and remaining cup cream until stiff peaks form. Fold egg whites into coconut cream mixture until fully incorporated.
Spread coconut mixture evenly over chilled chocolate and freeze, covered, at least six hours or up to two days. When ready to serve, use parchment overhang to lift and transfer s'mores to cutting board. Cut into 32 bars and top with shaved chocolate if desired. Makes 32 bars.