1. Bring vinegar to a simmer in a small saucepan over medium-low heat; cook until syrupy and reduced to 3 tablespoons (about 10 minutes), stirring occasionally. Remove from heat.
2. Combine oil, juice, pepper, and salt in a bowl, stirring with a whisk. Add salad greens; toss gently. Divide melon among 4 plates; top with salad greens. Arrange prosciutto and figs over salad greens; drizzle with balsamic syrup.