Bring vinegar to a boil in a small saucepan over medium-high heat. Reduce heat, and simmer until vinegar is reduced to 2 tablespoons (about 2 minutes). Remove from heat; stir in honey. Cool to room temperature.
Combine olive oil, pepper, and salt in a large bowl, stirring with a whisk. Add arugula, tossing gently to coat. Arrange arugula mixture on a platter. Top with peach wedges and prosciutto. Drizzle with balsamic syrup, sprinkle with cheese, and season with salt & pepper to taste.