Heat milk to boiling point in a saucepan. Cover pan and remove from heat. Whisk egg yolks and honey together in a bowl until thickened. Stir in vanilla and cinnamon. Slowly pour hot milk into the egg yolk mixture, whisking constantly. Return the mixture to a saucepan and cook over a low heat, stirring with a wooden spoon, until thickened slightly (coating the back of the spoon). Do not allow to boil.
Allow custard to cool to room temperature. Loosely cover the mixture with plastic wrap and refrigerate until cold (a minimum of 3 hours).
Freeze in an ice cream maker until just beginning to set. Stir in sour cream and freeze in the ice cream maker until set.