In a medium saucepan, mix the sugar, mint stems, ginger, and water over medium high heat, stirring until sugar dissolves. Bring to simmer for 2 to 3 minutes then remove from heat. Let the mixture steep 20 minutes before straining through a fine sieve. Chill the syrup. To serve, drizzle the chilled syrup over the watermelon cubes and garnish with fresh mint leaves.