Adapted from The Professional Pastry Chef
Heat the heavy cream and milk with the cinnamon stick to scalding. Do not let it boil. Remove from heat and set aside to infuse for 30 minutes.
Mix the granulated sugar and cinnamon in a medium-sized bowl. Use a hand mixer and beat until it's light and fluffy.
Gradually pour the cream and milk mixture into the whipped egg yolk mixture while whisking rapidly. Place a damp towel under the bowl to keep it from turning with the whisk.
Heat the mixture over simmering water, stirring constantly with a wooden spoon or whisk, until it thickens enough to coat the back of the spoon with a thin layer.
Do not overheat and break the custard. If this happens, just strain the custard to remove the chunks.
Stir in the vanilla extract.
Let cool to room temperature, then refrigerate covered until completely cold preferably overnight.
Remove the cinnamon stick.
Process the mixture in your ice cream freezer following the manufacturer's instructions.
Transfer to a chilled container and store, covered, in the freezer