Preheat the oven to 450 degrees . In a small bowl, stir together the parsley, garlic, butter, rosemary, 1/4 teaspoon salt and 1/8 teaspoon pepper. Gently lift the skin from the chicken and rub the butter mixture underneath; season the skin with salt. Place the chicken in a medium baking dish and roast until the skin is golden and the juices run clear, about 35 minutes.
Meanwhile, in a small bowl, whisk together the vinegar, hot water and mustard. Slowly whisk in the olive oil until emulsified and then stir in the chopped caramelized onions. Season with salt and pepper.
When the chicken is cool, remove the meat from the bones; discard the skin and bones. Shred the meat into thin strips and place in a large bowl along with the frisee and arugula. Drizzle the vinaigrette on top and toss to combine. Season to taste with salt and pepper. Mound the salad onto serving plates and scatter the remaining caramelized onions over the greens.