Preheat the oven to 325 (F).
Put 1 2/3 cups of milk and 1/4 teaspoon vanilla extract in a medium saucepan over medium heat and bring to a boil. Remove from the heat and let cool down very slightly.
Put 5 egg yolks, 1 cup sugar, 1/3 cup flour, 1/3 cup cornstarch and the remaining milk in a separate bowl and mix well to form a smooth paste.
Pour a little of the hot milk mixture into the egg mixture and stir well to combine. Pour the remaining milk mixture into the egg mixture and stir well until all the ingredients are combined.
Pour everything back into the saucepan over low heat and bring to a boil, whisking continuously with a whisk. Continue to do so until thick, about 10 minutes.
Pour the custard into a bowl, and lay plastic wrap directly on top (to stop a skin forming) and let cool completely on a wire rack.