Spray grill rack with nonflammable cooking spray. Preheat grill to medium heat (300° to 350°).
For salad: Brush peaches with 1 tablespoon oil. Cook until grill marks form, about 2 minutes per side. Remove from grill. Increase heat to medium-high (350° to 400°). Brush chicken with remaining 1 tablespoon oil; sprinkle with salt and pepper. Cook until a meat thermometer inserted in thickest portion registers 165°, about 5 minutes per side. Let rest on a cutting board for 5 minutes.
Cut chicken into ½-inch-thick slices. Arrange arugula, lettuce, peaches, and chicken on a serving platter. Sprinkle with cashews.
For dressing: In a medium bowl, whisk together honey, lime juice, vinegar, salt, ginger, black pepper, and red pepper. Slowly whisk in oil. Drizzle desired amount of dressing over salad. Serve with lime wedges. Store any remaining dressing in refrigerator for up to 2 days.
Recipe by Southern Lady Magazine at https://southernladymagazine.com/grilled-peach-and-chicken-salad-recipe/