Preheat your grill or grill pan to medium-high heat, aiming for around 400°F (200°C). Prepare your peach halves by washing and halving them, carefully removing the pits.

Lightly brush the cut sides of the peach halves with extra-virgin olive oil, then place the peaches cut side down on the hot grill. Grill for about 3-4 minutes until slightly softened and marked.

Remove the peaches from the grill and let them cool for a few minutes. Slice the grilled peaches into wedges.

In a bowl, combine extra-virgin olive oil, apple cider vinegar, honey, Dijon mustard, salt, and pepper to make the honey vinaigrette. Whisk until smooth.

In a large salad bowl, combine salad greens, thinly sliced red onion, half of the cheese, and nuts. Drizzle with honey vinaigrette and toss gently.

Arrange grilled peach wedges on top of the salad, sprinkle remaining cheese and fresh basil leaves over the salad.

Serve immediately, enjoying the colorful display and inviting aromas.