Preheat oven to 375 degrees. Season chicken with salt and pepper. Heat a large ovenproof skillet over medium-high; swirl in oil. Add chicken in a single layer, skin-sides down. Cook, flipping once, until browned on both sides, 8 to 10 minutes. Transfer to a plate.

Remove all but 2 tablespoons fat from skillet; reduce heat to medium. Add shallots and cook until softened, about 2 minutes. Add vinegar and boil 30 seconds. Add cranberry sauce and broth; simmer until reduced and thickened slightly, 2 to 3 minutes. Return chicken, skin-sides up, and any accumulated juices to skillet. Spoon enough of cranberry mixture over each leg to coat.

Transfer to oven and roast until a thermometer inserted into thickest parts of chicken (nearest but not touching bones) registers 165 degrees, 20 to 25 minutes. Spoon remaining cranberry mixture evenly over chicken; serve.