01 - Combine lemon juice, lemon zest, sugar, milk, vanilla extract, and ice cubes in a blender. Blend on high speed until completely smooth and frothy, approximately 45-60 seconds.
02 - In a clean, dry mixing bowl, beat egg white with cream of tartar using an electric mixer on medium-high speed until soft peaks form. Gradually add sugar while continuing to beat until glossy, stiff peaks form, approximately 3-4 minutes.
03 - Pour blended lemon mixture evenly into two tall glasses, filling approximately three-quarters full. Using a spoon or piping bag, dollop meringue generously on top of each frappé.
04 - Sprinkle additional lemon zest and crushed graham crackers over meringue topping. Serve immediately with straws and spoons. Optionally, toast meringue with kitchen torch until lightly browned.