01 - Combine cubed watermelon and lime juice in blender. Blend until completely smooth, approximately 30-45 seconds.
02 - Pour puree through fine-mesh sieve into pitcher, pressing with spoon to extract juice. Discard pulp for smoother consistency.
03 - Divide strained watermelon puree evenly among four tall glasses, filling each about one-third full.
04 - Place one generous scoop of vanilla ice cream into center of each glass, resting on top of puree.
05 - Slowly pour chilled lemon-lime soda over ice cream, pouring down side of glass to control foam and allow gradual mixing.
06 - Top with fresh mint leaves and watermelon balls or slices. Serve immediately with straw and long spoon for stirring.