Line the bottom of a 9 inch square dish with parchment or foil. Place graham crackers flat in the pan. Break them to fit.
Heat 1/3 cup cream for 1 minute in the microwave and pour over the chocolate chips. Stir together until smooth. Pour half over the graham crackers and place into the freezer while preparing the ice cream filling.
Whip the egg whites until frothy then add the sugar. Whip until stiff peaks form. Add a few drops of green food coloring if desired and the mint extract.
Whip the heavy cream until stiff peaks form. Fold in the egg whites and then layer it over the chocolate.
Top with the remaining chocolate and graham cracker pieces.
Cover and freeze for at least 6 to 8 hours or overnight. Cut up and serve.