Cut the watermelon into 1-inch cubes, removing any seeds as you go. Spread the cubes in a single layer on a paper-lined tray and freeze for at least 3 hours, or ideally overnight, until completely solid. Freezing the watermelon first is essential because it gives the sorbet its creamy, scoopable texture without requiring an ice cream maker.
Add the frozen watermelon cubes to a food processor along with the syrup, lime juice, kosher salt, and vodka if using. Blend for 1 minute to break down the frozen chunks, then scrape down the sides of the bowl. Continue blending for 4 to 6 minutes, scraping as needed, until the mixture transforms into a smooth, creamy sorbet consistency. The vodka helps maintain a softer, more scoopable texture by lowering the freezing point slightly—I find it makes a noticeable difference in the final texture, even though it's optional.
Fold the finely minced fresh mint into the blended sorbet until evenly distributed. Serve immediately for a soft, granita-like texture, or transfer to a shallow freezer-safe container and freeze for 2 to 3 hours for a firmer, more traditional sorbet consistency. Fresh mint adds brightness that perfectly complements the watermelon and lime—I always use it freshly minced right before serving so the flavor stays vibrant.