01 - Preheat a grill or grill pan to medium-high temperature.
02 - Brush peach halves with 1 tablespoon olive oil. Place cut-side down on the grill and cook for 2 to 3 minutes until grill marks form and the fruit softens slightly. Remove and let cool, then slice into wedges.
03 - In a small bowl, whisk together the remaining olive oil, honey, sea salt, and black pepper.
04 - Arrange the arugula evenly on a large serving platter.
05 - Top the greens with grilled peach wedges, halved cherry tomatoes, and thinly sliced shallot.
06 - Gently tear burrata into large pieces and distribute over the salad mixture.
07 - Drizzle salad with prepared dressing and balsamic glaze. Sprinkle toasted nuts and garnish with torn basil leaves, if desired.
08 - Present immediately while peaches remain slightly warm.