Heat balsamic vinegar in a small saucepan over medium-high heat. Bring to a gentle boil, stirring occasionally, and cook until the liquid is reduced by one half.
⅓ cups balsamic vinegar
Drizzle about half of the balsamic glaze onto a serving platter and carefully arrange half of the watermelon squares on top.
Transfer some of the whipped cheese to a pastry bag fitted with a large tip (or use a plastic sandwich bag with one of the bottom corners removed). Pipe some whipped cheese onto each watermelon square on the platter and top each with some fresh basil.
12 fresh basil leaves
Place another slice of watermelon on top of the basil and gently press down to secure. Top each appetizer with some of the remaining whipped cheese. Sprinkle with chopped pistachios.
⅓ cup pistachios
Serve immediately garnished with small sprigs of fresh basil and a light drizzle of the remaining balsamic glaze.