Preheat a grill or grill pan to medium‑high heat.

Brush the peach halves with a tablespoon of olive oil and season with a pinch of salt and pepper.

Place the peaches cut‑side down on the grill and cook for 3–4 minutes, until grill marks appear and the flesh is slightly softened.

While the peaches grill, whisk together the remaining olive oil, honey, lemon juice, lemon zest, salt, and pepper to make a bright vinaigrette.

As soon as the peaches are done, transfer them to a plate and let them rest for a minute; then sprinkle each half with a pinch of salt.

In a large bowl, combine the arugula, toasted almonds, and torn basil; drizzle with the vinaigrette and toss gently to coat.

Divide the dressed greens among four plates, nestle a grilled peach half on each, and place a burrata ball on top of the peach.

Finish by drizzling a little extra honey or a splash of balsamic glaze if desired, and serve immediately while the burrata is creamy and the peaches are warm.