Cut the prosciutto slices in half or in thirds if they are very long.
Cut chunks of feta cheese about the same length as the peach slices.
Hold a peach slice and a piece of feta cheese together and wrap snuggly with a slice of prosciutto.
Repeat until all of the peach slices are covered.
Brush both sides of the wrapped peach and feta with olive oil.
Place 3-4 at a time into a hot skillet on the stove or the grill.
Grill for 1-2 minutes on each side.
Remove from grill or skillet and drizzle with balsamic vinegar or balsamic glaze.
Garnish with fresh basil and serve.