1. Combine milk and cinnamon in top of a double boiler over simmering water. Cook, stirring every 10 to 15 minutes, until milk has reduced by almost half and is thick and amber in color, 1 1/2 to 2 hours.

2. Remove from heat; discard cinnamon stick. Beat with a wooden spoon. Transfer to a clean bowl, cover, and refrigerate up to several weeks, until ready to use.