In a mixing bowl, whisk together the egg yolks and sugar until pale and thick.
In a saucepan, heat the milk and heavy cream until it just begins to simmer. Do not boil.
Slowly pour the hot milk mixture into the egg yolk mixture, whisking constantly.
Return the mixture to the saucepan and cook over low heat, stirring constantly, until it thickens and coats the back of a spoon.
Remove from heat and stir in the cinnamon and vanilla extract.
Let the mixture cool to room temperature, then refrigerate until completely chilled.
Pour the chilled mixture into an ice cream maker and churn according to the manufacturer's instructions.
Transfer the ice cream to a container and freeze until firm, about 2 hours.