While the duck is roasting, return the pan to medium-high heat. Add shallot and cook, stirring constantly, until fragrant, 30 seconds to 1 minute. Add pomegranate juice and bring to a boil. Reduce heat to a simmer; cook until reduced by half, 1 to 2 minutes. Stir broth and cornstarch in a small bowl until the cornstarch dissolves. Add to the pan. Bring to a boil, stirring constantly. Reduce heat to a simmer and cook, stirring, until the sauce is thickened, 1 to 2 minutes. When the duck has finished resting, pour any accumulated juices into the sauce and stir to combine.