Pour the cider or juice into a 5-quart or larger slow cooker.
Cut the orange into 1/4-inch-thick rounds. Cut the ginger into 1/4-inch-thick slices. Add both to the slow cooker.
Add the cinnamon sticks, cloves, and star anise. To make it easier to serve, place the cloves and star anise pods in a tea ball first, or place in a double layer of cheesecloth or coffee filter, gather it up into a sachet, and tie closed with kitchen twine.
Cover the slow cooker and cook until the flavors meld, 4 hours on LOW. Add the bourbon, brandy, or rum and stir to combine. Let sit for 10 minutes for the flavors to meld. Keep warm and serve in mugs garnished with orange slices.