Heat the grill to medium. Brush the peach halves with 1/2 tablespoon olive oil.

Grill peaches cut-side down for 3 to 4 minutes, until grill marks form. Remove and cool slightly.

Toss arugula with the remaining olive oil, salt, and pepper. Spread on a platter.

Tear burrata into pieces and place over the arugula.

Slice peaches and add on top. Drizzle with balsamic glaze. Serve right away.