Preheat oven to 450 degrees. On a rimmed baking sheet, toss sweet potato and cauliflower with 1-1/2 tablespoons of oil and season with salt and pepper. Roast until cooked through and browned on one side, about 25 minutes. Transfer to a bowl and gently toss with 1 tablespoon vinegar.
Meanwhile, in a large nonstick skillet, heat 1/2 tablespoon oil over medium-low heat. Season chicken with salt and pepper. Cook until golden and cooked through, 30-35 minutes, flipping chicken halfway through. Transfer chicken to a plate and tent with foil to keep warm.
To skillet, add broth, thyme, and 1 tablespoon vinegar. Cook over medium-high, scraping up browned bits, until reduced by half, 3-5 minutes. Return chicken and any accumulated juices to skillet and turn chicken to coat with sauce. Remove from heat and stir in butter. Serve chicken with vegatbles and pan sauce.