For a classic cranberry syrup, leave out the spices, but keep the orange peel and juice.
In a medium saucepan, combine the cranberries, cranberry juice, sugar, orange peels, fresh orange juice, cinnamon sticks, cloves, star anise, nutmeg, and Grand Marnier.
Place over low heat, stirring occasionally until the sugar has completely dissolved.
Allow the mixture to gently simmer over low heat for 15–20 minutes, until the cranberries begin to burst and the syrup becomes fragrant and infused with the spices.
Remove from the heat and allow the syrup to steep for an additional 10–15 minutes.
Strain through a fine-mesh strainer, gently pressing the cranberries to release their juices.
Allow to cool completely before using. Store in an airtight container in the refrigerator for up to 2 weeks.