Carefully add the chicken broth, cover quickly, and cook until all but about 1 tablespoon of the broth has evaporated, about 2 minutes. Uncover, reduce the heat to medium low, and add the pomegranate mixture (re whisk, if necessary) and the cayenne. Cook, stirring gently, until the mixture reduces and becomes slightly glazy, about 1 minute. Take the pan off the heat, add the chilled butter, and gently toss with a heatproof spatula until the butter has melted, 30 seconds to 1 minute. Season to taste with salt.