Heat the cider in a large pot over medium heat until it starts to simmer. Add 3 strips of orange zest, the orange juice, brown sugar, and pumpkin pie spice and stir. Bring to a simmer then turn the heat down to low to keep it hot, but not simmering. Heat for 5 minutes to allow all of the flavors to meld together before serving.
Serve hot in heatproof mugs with a shot of spiced rum, if desired.