Using a vegetable peeler, remove the zest from the orange in wide strips; reserve one strip for each drink and refrigerate, covered, until serving time. Stick the cloves into two or three of the remaining zest strips and set aside. (Reserve the orange for another use.)
In a large saucepan over medium heat, warm the allspice and cinnamon sticks, stirring, until fragrant, 1 to 2 minutes. Remove from the heat and carefully add the cider (it will sputter vigorously), cranberry juice, brown sugar, and the clove-studded orange zest strips. Adjust the heat to medium-high and bring to a simmer, partially covered and stirring occasionally, to infuse the cider mixture, about 20 minutes. Cover the pot completely, remove from the heat, and let steep for 20 minutes more.
Set a fine-mesh strainer over a large heatproof bow. Pour in the cider, discard the solids, and return the mixture to the saucepan. Over medium heat, return the cider to a simmer. Add the vanilla, stir, taste, and adjust the seasoning with additional brown sugar if necessary.
