1) Line the bottom of a 9-in.-square baking pan with parchment paper, leaving an overhang on two sides. Place graham crackers in the bottom of the pan, cutting them to fit as necessary.
2) Heat 1/3 cup of the cream in a small saucepan until it barely begins to simmer; remove from heat. Add the chopped chocolate and stir until the chocolate is melted and the mixture is smooth. Spread the chocolate mixture evenly over the graham crackers. Freeze for 10 minutes.
3) Meanwhile, using an electric mixer, beat the egg whites in a large bowl until frothy. Gradually add the sugar and beat until stiff, glossy peaks form; set aside. In a separate large bowl, using the electric mixer (no need to clean the beaters), beat the cream of coconut and the remaining cup of cream until stiff peaks form. Fold the egg whites into the coconut-cream mixture until fully incorporated.
4) Spread the coconut mixture evenly over the chilled chocolate and freeze, covered, for at least 6 hours or up to 2 days. When ready to serve, use the parchment overhangs to lift and transfer the s’more to a cutting board. Cut into 32 bars and top with shaved chocolate, if desired.