In a blender, combine egg whites, sugar, heavy cream, whole milk and vanilla until blended. Refrigerate for at least one hour or up to 24 hours.

Pour egg mixture into the base of an ice cream maker. Process according to manufacturer's directions, adding chopped strawberries during the last few minutes of churning.

Meanwhile, line an 8 x8 in pan with two sheets of plastic wrap that are arrange like a cross. Be sure to allow enough over hang so that the sandwiches will be easy to remove.

Line 9 graham cracker halves in the pan. Pour ice cream over crackers and top with remaining 9 crackers. Loosely cover sandwiches and place in the freezer until set.

Carefully remove the ice cream sandwiches using the plastic wrap as handles. With a knife, section out each ice cream sandwich.

Wrap each individual sandwich with plastic wrap and place them in the freezer until ready to serve.