Preheat the oven to 375 degrees F. Heat 2 tablespoons vegetable oil in a large ovenproof skillet over medium-high heat. Season the chicken with 1 teaspoon salt and a few grinds of pepper. Add to the skillet skin-side down and cook until golden, about 5 minutes. Pour off most of the fat from the skillet; transfer the skillet to the oven (do not flip the chicken). Roast 5 minutes, then flip the chicken and roast until cooked through, about 15 more minutes.
Meanwhile, cook the bacon in the remaining 1 tablespoon oil in a large pot over medium-high heat until crisp, about 5 minutes. Remove with a slotted spoon and drain on paper towels, reserving the drippings in the pot.
Add the mushrooms, carrots, parsnips, turnips, red onion, 2 tablespoons water, 1/2 teaspoon salt and a few grinds of pepper to the pot. Cook, stirring occasionally, until the vegetables are tender, about 12 minutes. Return the bacon to the pot along with the parsley and thyme. Serve the chicken with the vegetables.