Combine the apple cider, cranberry juice, cinnamon sticks, cloves, and star anise in a large pot.

Add the orange wheels.

Bring the mixture to a gentle simmer over medium heat, uncovered, for 5 to 7 minutes, watching for small bubbles breaking the surface; a full rolling boil will turn the citrus bitter, so pull back the heat before it gets there.

Reduce the heat to low and let the cider steep for 15 minutes, stirring occasionally, until the kitchen smells like a spice rack and the liquid has turned a deep amber.

Strain out the spices and orange, or leave them in for a rustic, floating look.

Ladle the hot cider into heatproof mugs.

Garnish each mug with a cinnamon stick and a clove-studded orange wheel.