Five-Spice Ice Cream

Tear tangerine peel into pieces. Pulse peppercorns, star anise, cloves, and allspice to a coarse mixture in grinder. Combine cream, milk, tangerine peel, spices, and 1/2 cup sugar in a heavy medium saucepan. With tip of a paring knife, scrape seeds from vanilla bean into cream mixture, then drop in pod. Bring mixture just to a boil over medium heat. Remove from heat and let steep, covered, 20 minutes. Bring spiced milk to a simmer, then strain through a fine-mesh sieve into a bowl, discarding spices and peel. Return to saucepan. Whisk whole egg and yolks with remaining 1/2 cup sugar in bowl until pale, then add hot spiced milk in a slow stream, whisking. Return to saucepan and cook, stirring with a wooden spoon, until mixture coats back of spoon and registers 170 to 175 °F on an instant-read thermometer (do not let boil). Immediately strain custard through fine-mesh sieve into a bowl, then whisk in rum and kosher salt. Chill custard at least 6 hours, then freeze in ice cream maker.