Slice fresh peaches into wedges and place them in a clean jar. In a saucepan, combine white balsamic vinegar, white vinegar, kosher salt, and honey. Heat until dissolved, then stir in cold water. Pour over peaches and let pickle for 30 minutes.

Retrieve pickled peaches, drain excess liquid, and wrap each wedge in a slice of prosciutto. Thread onto skewers, alternating with a mozzarella pearl and fresh basil leaf.

In a bowl, whisk pickling liquid, olive oil, minced garlic, rosemary, and thyme. Season with salt and pepper.

Arrange skewers on a platter, drizzle dressing over them, and garnish with basil leaves and cracked pepper. Serve immediately.