Heat grill or grill pan to medium-high and brush peach halves with 1 tbsp olive oil.

Grill peaches cut-side down 3–4 minutes until char marks appear; cool slightly.

Whisk remaining olive oil, balsamic, honey, salt, and pepper in a bowl.

Toss arugula with half the dressing in a serving bowl.

Halve burrata and arrange on greens; place grilled peaches around it.

Drizzle remaining dressing over salad and sprinkle almonds if using.