In the container of a blender, add the lime juice, simple syrup, mint, club soda, and rum. Fill the container with ice and blend on high until the ice is crushed.
Pour into two tall glasses and garnish each with a sprig of mint.
Notes
Simple syrup is simple: combine equal parts sugar and water and simmer until dissolved; cool the syrup before using.
Recipe by Acadiana Table at https://acadianatable.com/2024/07/15/frozen-mojito/