Bring the vinegar to a simmer in a 2-quart nonreactive saucepan over medium heat. Simmer until glossy and reduced to 3 Tbs., about 10 minutes. Pour the reduced vinegar into a small bowl and let cool to room temperature.Meanwhile, in a medium bowl, sprinkle the strawberries with the sugar and pepper (if using) and toss gently until combined. Let stand, stirring once or twice, until the sugar dissolves and the berries release some juice, 10 to 15 minutes. Put a scoop of ice cream in each of 4 parfait glasses or bowls. Top each with about 1/4 cup strawberries and their juices, drizzle with about 1 tsp. balsamic syrup, and sprinkle with about 1/2 Tbs. pine nuts. Repeat with the remaining ingredients. Serve immediately.