Step 1: In a large blender, combine the cubed watermelon, fresh lime juice, and granulated sugar (if using). Blend until completely smooth.
Step 2: Place a fine-mesh sieve over a large pitcher or bowl. Pour the blended watermelon mixture through the sieve, pressing with a spoon or spatula to extract as much liquid as possible. Discard the pulp. This step ensures a smooth, pulp-free limeade.
Step 3: Gently muddle the 1/4 cup of fresh mint leaves in the bottom of the pitcher. You want to bruise the leaves just enough to release their aromatic oils, not tear them apart.
Step 4: Pour the strained watermelon-lime concentrate into the pitcher with the muddled mint. Stir well to combine. Taste and adjust sweetness or tartness if desired, adding more sugar or lime juice as needed.
Step 5: Refrigerate the concentrate for at least 30 minutes to chill thoroughly and allow the mint flavors to meld. For best results, chill for 1-2 hours.
Step 6: To serve, fill individual glasses with ice. Pour about 1/2 to 3/4 cup of the watermelon-lime concentrate into each glass, depending on your preferred strength.
Step 7: Top each glass with chilled sparkling water or club soda. Gently stir. Garnish with a fresh mint sprig, a lime slice, and a small watermelon wedge. Serve immediately and enjoy your refreshing summer drink!