Spread watermelon cubes on a tray lined with plastic wrap or parchment (for easiest removal) and chill in freezer until frozen.
Add sugar to lime juice and stir to combine; sugar should dissolve in a minute or two.
Place frozen watermelon, sweetened lime juice, and rum in blender and blend until thick but smooth.
Add mint and pulse a few more times, so that is chopped but not pureed.
Pour into two glasses.
Top with a splash of seltzer if you wish, finish with lime wedges and extra mint.
Repeat all summer.
