01 - Set a grill or grill pan to medium-high heat and allow it to reach full temperature before cooking.
02 - Lightly brush the chicken breasts and peach halves with 1 tablespoon of olive oil, then season generously with salt and freshly ground black pepper.
03 - Place the chicken on the grill and cook for 5 to 7 minutes per side until fully cooked through and juices run clear. Grill the peach halves cut-side down for 2 to 3 minutes until prominent grill marks develop and the fruit softens slightly. Remove both from the grill and let rest.
04 - Place the chopped kale in a large mixing bowl. Drizzle with 1 teaspoon of olive oil and a pinch of salt, then massage the leaves firmly with your hands for 1 to 2 minutes until they become tender and turn a deeper vibrant green.
05 - In a small bowl, whisk together the remaining olive oil, balsamic vinegar, honey, Dijon mustard, minced garlic, salt, and pepper until the dressing is smooth and well emulsified.
06 - Slice the rested grilled chicken breasts into even strips and cut the grilled peach halves into wedges.
07 - Add the sliced chicken, grilled peaches, red onion, torn basil, and toasted nuts to the massaged kale. Drizzle with the honey-balsamic dressing and toss gently until all components are evenly coated.
08 - Scatter crumbled feta cheese over the top if desired. Serve immediately while the peaches are still slightly warm.