In a large pot of boiling water, cook the carrots, parsnips, and corn until the carrots are crisp-tender, about 5 minutes. Drain well.

Meanwhile, in a small bowl, combine the brown sugar, garlic, paprika, mustard, ginger, cayenne, and 1/4 teaspoon of the salt. In a large bowl, combine 1 1/2 tablespoons of the brown sugar mixture, the vinegar, apple juice, ketchup, oil, and the remaining 3/4 teaspoon salt. Set the dressing aside.

Preheat the grill. Using your fingers, gently separate the skin from the chicken meat, leaving one side attached. Sprinkle the remaining brown sugar mixture over the chicken flesh and replace the skin. Place the chicken on the grill, skin-side up. Cover and grill at medium, or 6 inches from the heat, turning the chicken every 6 minutes, for 18 minutes, or until the chicken is cooked through. When the chicken is cool enough to handle, remove and discard the skin and shred the meat with your fingers.

Add the shredded chicken to the bowl of dressing along with the carrots, parsnips, corn, and scallions, tossing to combine. Divide among 4 plates, sprinkle the pecans over, and serve warm or at room temperature.