Using tongs, burn the cinnamon sticks over an open flame for 5 to 10 seconds. Alternatively, place the sticks on a sheet pan and char them with a blowtorch. Then, in a mortar and pestle, coarsely grind the torched cinnamon sticks with the nutmeg.
Add the remaining ingredients and continue to pound the spices until coarsely ground. Use immediately or store the rub in an airtight container at room temperature for up to 1 year.