Marinate the chicken. Use a whisk to combine the shallots, mustard, salt, juice concentrate, vinegar, olive oil, and black pepper in a nonreactive bowl. Pour 1 cup of the prepared dressing into another nonreactive bowl and stir in the chili paste to create the marinade. Chill the remaining dressing until needed. (The dressing improves if assembled several hours before serving.) Rinse and pat the chicken dry, and place in a nonreactive dish. Season the chicken on both sides with black pepper and pour the marinade over the pieces, coating well on both sides. Cover the dish and refrigerate for up to 24 hours.
Prepare the salad. Place a doubled sheet of paper towels on a plate and set aside. Melt the butter in a 10- to 12-inch heavy-bottomed skillet over medium heat and, when hot and bubbling, stir in the nuts. Cook, stirring constantly, until fragrant and light golden, about 2 minutes. Pour the nuts onto the prepared plate and shimmy them to remove the excess butter. Remove the paper, leaving the nuts on the plate, and sprinkle them lightly with salt. Set the nuts aside.
Take the chicken out of the refrigerator 30 minutes before grilling. Heat an outdoor gas grill on high or heat a charcoal grill to the gray ash stage. Alternatively, heat a large stove-top grill-pan until very hot, with your overhead exhaust fan turned on. When hot, oil the rack to your grill or your grill pan and, after letting the oiled surface heat for a minute or so, lay the marinated chicken pieces on the hot surface (discard the marinade). Grill the chicken until golden on each side and the meat is cooked through but still succulent, 6 to 10 minutes. Remove the chicken to a plate and let it rest for 5 minutes, tented loosely with aluminum foil.
Slice the chicken into diagonal strips and sprinkle the pieces lightly with salt. Place the greens in a large mixing bowl and lightly coat with some of the reserved dressing. Add the grapes, pears, apples, and half of both the cheese and the toasted nuts. Toss the mixture gently but thoroughly, then divide the salad among individual serving plates and scatter the remaining cheese and nuts lightly over the top. Arrange several slices of grilled chicken either on top or around the salad and serve immediately, with any additional dressing passed separately at the table.