Bring milk, sugar, and cinnamon sticks to a boil in a large saucepan over low heat. Continue to boil, stirring constantly, until milk has reduced by a little more than one-third, about 20 minutes. Remove from the heat. Leave in the saucepan and allow to cool slightly, about 10 minutes.

Beat egg yolks with an electric mixer until thick and pale. Mix in a little of the warm milk mixture. Pour egg yolk mixture into the saucepan with the remaining milk mixture. Stir to combine and bring to a boil over low heat. Stir constantly, scraping the bottom and sides, until mixture is thick enough to coat the back of a spoon, 5 to 7 minutes.