Preheat your oven to 180°C (350°F).
In a saucepan, heat the milk and cinnamon stick over medium heat until it's hot but not boiling. Remove the cinnamon stick and discard it.
In a separate bowl, whisk together the eggs, sugar, cornstarch, and flour until smooth.
Gradually pour the hot milk into the egg mixture, whisking constantly.
Return the mixture to the saucepan and cook over low heat, stirring continuously, until it thickens and comes to a gentle boil. This should take about 5-7 minutes.
Remove the mixture from the heat and stir in the vanilla extract.