Place the cider, cinnamon stick, star anise and lemon and orange slices into a large saucepan and bring to a boil.
Reduce heat to medium-high and simmer for about 20 minutes to allow flavors to combine.
Carefully pour the liquid through a mesh strainer into a large, glass heat-safe bowl.
Add the rum to the bowl and stir to combine.
Ladle rum into heat-safe glasses, such as high ball glasses.
Garnish each glass with a slice of orange, dollop of vegan-soy-free whipped cream, star anise and cinnamon stick.