Put milk and cream into a small saucepan. Carefully heat the liquids, stirring often, until they start to boil. Remove from heat and add the two cinnamons. Cover and set aside to infuse for about an hour.
Combine sugar and egg yolks in a small bowl. Whisk together until thoroughly mixed and the yolks lighten in color.
Slowly whisk the milk mixture into the egg mixture. When combined and smooth, return the mixture to the saucepan. Stirring continuously, heat the mixture over medium heat until it begins to thicken and easily coats the back of a wooden spoon.
Strain the mixture into a bowl set in an ice bath. Stir mixture until it is chilled.
Freeze mixture in an ice cream machine. Harden in a freezer.
Move the ice cream to a refrigerator for about an hour before serving.