Step 1

Place orange in a large saucepan and pour in cold water to come 1" up sides of pan. Bring to a boil, then remove immediately from heat and drain orange in a mesh sieve or colander. Rinse under cold water; return to saucepan. Add cranberries, sugar, butter, cinnamon, allspice, and salt and bring to a boil, stirring to dissolve sugar.

Step 2

Cook, stirring often and reducing heat as needed to avoid scorching, until cranberries burst, juices are syrupy, and pan is visible when a wooden spoon is dragged across the bottom, 12–15 minutes. Let cool.

Step 3

Do Ahead: Sauce can be made 1 week ahead. Cover and chill.