Put the watermelon cubes on a baking sheet lined with parchment. Freeze until frozen.
Add the frozen watermelon to a food processor. Add the Simple Syrup and 1/2 cup water and blend. Scrape down the sides and continue to blend until smooth.
Serve as is, or add tequila or bourbon and garnish with fresh mint leaves if desired. Or wet the rim of the glasses with the lime wedges and dip in salt if desired. Or add a squeeze of lime juice.
Combine the sugar and 1 cup water in a small saucepan and bring to a boil. Cook, stirring, until the sugar dissolves. Remove from the heat and let cool completely. Keep covered in the refrigerator up to 1 month.