Step 1

In a medium bowl, use a rubber spatula to combine the butter, sugar, and apple pie spice. (This mixture can be made ahead and stored in the refrigerator for up to 1 week. Let it soften at room temperature for 30 minutes before mixing the drinks.)

Step 2

Add 2 tablespoons of the spiced butter mixture to each of the 6 mugs. Pour about 3/4 cup of very hot water into each mug, over the butter; stir to combine. Add 2 ounces of rum to each mug and stir.

Step 3

Press 1 clove into the rind of each orange quarter. Add an orange quarter to each mug, plus 1 star anise pod and a cinnamon stick for more spice, if you like. Serve immediately.