01 - Combine lemon juice, lemon zest, sugar, milk, vanilla extract, and ice cubes in a blender. Blend until completely smooth and frothy, approximately 30-45 seconds.
02 - In a clean, dry bowl, beat egg white with cream of tartar until soft peaks form. Gradually add sugar while beating continuously until glossy, stiff peaks form, about 3-4 minutes.
03 - Divide blended lemon mixture evenly between two tall glasses. Spoon or pipe meringue generously on top of each frappé, creating peaks.
04 - Sprinkle with additional lemon zest and crushed graham crackers if desired. Serve immediately with straws and spoons. For toasted meringue, briefly torch topping until golden brown.