Mint Simple Syrup: In a small saucepan, combine 1/2 cup water, 1/2 cup granulated sugar, and mint leaves. Bring to a simmer for about 3 minutes until the sugar is dissolved. Set aside and let cool before using. See notes if using store-bought or regular simple syrup.
Add watermelon to a blender and blend on medium-high until pureed. Use a fine mesh strainer to remove the pulp from the juice, straining the juice into a pitcher or large measuring cup.
To the juice, add 1/2 cup of the mint simple syrup and vodka. Stir to combine.
Assemble the cocktail by filling a glass with ice and adding 1/2 cup of the cocktail mixture. Top off the cocktail with approximately 1/2 cup club soda (more or less to taste). Garnish with additional watermelon cubes and fresh mint as desired.
To use regular simple syrup: before adding ice to the glasses, place 2 tablespoons of mint leaves in the bottom of the glass and muddle with approximately 1 tablespoon of the cocktail mixture. Continue assembling the cocktail as directed.If you have leftover simple syrup, store it in an airtight container in the fridge for up to 1 week.To make without a blender (original method): as referenced in the video, use a fine-mesh strainer and a large spoon or muddler to press the juice out of the watermelon in batches until you have 1 cup of juice. Continue assembling the cocktail mix and cocktails as directed.