In a small saucepan over medium high heat, combine Granulated Sugar (1/2 cup), Water (1/2 cup), and the Fresh Mint Leaves (1/2 cup) stirring occasionally until sugar is dissolved. Remove from heat. Let steep for 10 minutes. Strain mint leaves from syrup. Discard.
Add the Seedless Watermelon (4 cup) to the blender, and puree until very smooth. Place a fine mesh sieve over a small bowl or 4 cup measure. Strain pulp from juice through the sieve, pressing on the solids with the back of a spoon. Discard the solids.
Chill juice, simple syrup, and Club Soda (to taste) at least 4 hours, until very cold.
For individual drinks, mix 3/4 cup watermelon juice with 1-2 tablespoons simple syrup. Add 1/4 to 1/2 cup club soda (to taste) and a squeeze of Lime (1).