In a food processor, combine 1/2 cup of the mint leaves and the sugar and process until well blended. Add the chili, vinegar and lime juice and process again. With the motor running, drizzle in the olive oil. Transfer the vinaigrette to a bowl and season with a pinch each of salt and pepper.
Place the watermelon and cheese in individual bowls and drizzle with the vinaigrette. Garnish with the remaining 1/4 cup mint leaves and serve immediately.