Place the quartered apples, cinnamon sticks, whole cloves, star anise, and sliced orange into a large Dutch oven, leaving the apples unpeeled and uncored so the skins and cores add color and pectin. Add enough water to cover the fruit and spices.

Bring the mixture to a boil over high heat, then immediately reduce to a low simmer. Keep it simmering uncovered for 2 hours until the apples are very soft and the liquid is flavorful.

Mash the softened apples with a potato masher while they are still in the simmering liquid. Simmer uncovered for 30 more minutes to further break down the fruit.

Strain the cider through a fine-mesh sieve, pressing the pulp firmly to extract all the liquid. Discard the solids.

Stir in the brown sugar or maple syrup and the vanilla extract, then taste and adjust the sweetness to your preference. Heat gently for 2 minutes if needed to dissolve sweetness, keeping the mixture at a low simmer.

Serve the apple cider warm in mugs, garnished with additional cinnamon sticks and orange slices. Let it sit 1 minute so the spices settle before sipping, and enjoy with visible steam rising.