Preheat the oven to 450°F.
Season the thighs with the salt and pepper. Heat a large heavy roasting pan or heavy skillet over medium-high heat. Add 2 tablespoons of the oil and swirl to coat the bottom. When the oil is hot, add the thighs skin side down. Brown, turning once, about 10 minutes. Transfer the thighs to a platter and set aside.
Prepare the parsnips and celery: peel and roll-cut into 1-inch lengths or cut conventionally.
Add the remaining oil to the pan, swirl, and heat. When the oil is hot, add the onions, ginger, parsnips, celery and thyme. Season with salt and pepper and sauté the vegetables, stirring, until softened, about 6 minutes. Top with the thighs, skin side up, and bake uncovered until the chicken and vegetables are done, 30 to 40 minutes. Transfer to a platter or four individual serving plates and serve.