Mix together all ingredients for the BBQ rub in a small container. You will likely have some left over, so mix it in a container that you can seal and store any remainder.
Cut the chicken breasts in half horizontally so you end up with 4 thinner cutlets. Season liberally with the BBQ rub mixture leaving at least 1 1/2 tsp of the BBQ rub for the vinaigrette. Let the chicken sit with the rub while you prepare the vegetables and vinaigrette.
Cut the cabbage, peaches, carrots, and green onions. Using a knife, shred the cabbage as thinly as possible. Wash and dry in a salad spinner.For the peaches, wash them and cut away from the seed then cut into thin slices. For the carrots, wash, peel, and cut into matchstick size pieces using a knife or julienne peeler (which is a favorite tool of mine!) For the green onions, wash and cut into matchstick sized pieces by cutting in quarters lengthwise and then into about 2 inch pieces. Toss the cabbage, peaches, carrots, and green onions together in a bowl.
Whisk together the cider vinegar, honey, Dijon mustard, and BBQ rub. Slowly drizzle in the olive oil whisking while you are drizzling to ensure the vinaigrette remains emulsified.
Heat a grill pan or cast iron skillet over medium high heat until the pan is hot. Add bit of oil to the pan. Cook the chicken for about 4 minutes on each side until the internal temperature reaches 165F degrees. Set aside to cool slightly.
On a large platter or in a large bowl, add the salad vegetables. Slice the chicken breast into long strips and place on top of the salad. Drizzle with some of the vinaigrette. Top with crispy French fried onions. Serve with extra vinaigrette on the side.
Any remainder BBQ rub is great to have on hand for seasoning chicken, pork, or fish.
For the BBQ sauce vinaigrette, I think a sweet and smoky BBQ sauce works best here. I used Sweet Baby Rays.