Peel and pit peaches; cut into quarters. Transfer into a medium container or large jar and add thyme.
In a small pan add apple cider vinegar, white balsamic vinegar, water, salt, and honey. Bring to a boil, then reduce heat and stir until fully combined and honey is dissolved. Pour liquid over the peaches; ensure they are fully submerged. Set aside for 30 minutes.
Remove the peach slices; reserve pickling liquid. Skewer the peaches onto a wooden pick with IL Villaggio Prosciutto Crudo and IL Villaggio Ovoline Mozzarella. Add basil, if desired. Drizzle honey to finish and serve.