Mix all the ingredients together in the small saucepan including the orange peel.
Place on the stove on medium heat and bring to a simmer, stirring occasionally.
Reduce heat to low and simmer for about 15 minutes, until the cranberries begin to pop. Smash some of the berries to help thicken the sauce.
Remove the cinnamon sticks, star anise, and orange peel from the pot.
If you prefer a smoother consistency, smash the majority of the berries with the back of the spoon (a potato masher also works well for this). You can even use an immersion blender to get a super smooth consistency. It's up to you and your preference!
Remove the cranberry sauce from the stove, transfer to a heat-proof dish, and let cool completely in the fridge. The sauce will thicken further as it cools.
Enjoy as a tasty side dish with your holiday meal!