Finely chop the shallot.

Heat the oil in a medium saucepan over medium-high heat. Add the shallot and cook until slightly softened, 2-3 minutes. Stir in the cranberries, granulated and brown sugars, cider, cinnamon, and allspice.

Bring mixture to a boil, then reduce heat to medium and simmer, stirring occasionally, until cranberries have popped and the sauce thickens slightly, about 8 minutes.

Meanwhile, peel, core, and cut the apple into a 1/4-inch dice.

Stir the diced apple into the sauce and cook until slightly softened, about 2 minutes. Remove from heat and let cool to room temperature.

Chill sauce for at least 3 hours before serving to thicken.