Preheat your grill to medium-high heat.
In a small bowl, mix together the olive oil, salt, and black pepper. Rub this mixture all over the skirt steak.
Place the skirt steak on the grill and cook for about 3-4 minutes on each side for medium-rare, or until your desired doneness is reached.
While the steak is grilling, slice the peaches and set them aside.
Once the steak is done, remove it from the grill and let it rest for about 5 minutes.
Slice the steak against the grain into thin strips.
On a serving platter, arrange the sliced steak and top with the fresh peach slices.
Tear the burrata cheese into pieces and scatter it over the steak and peaches.
Drizzle balsamic glaze over the top and garnish with fresh basil leaves.