Bring the milk and the butter to a boil. Remove from heat, stirring occasionally (3-5 minutes) cooking the mixture slightly.
In a bowl, combine sugar, flour, eggs, and egg yolks, whisk into a soft paste.
Whisk paste as you slowly pour in the milk mixture. Continue to whisk until fully combined into a smooth liquid. Stir in the vanilla and rum. Refrigerate 12 to 24 hours.
Once ready to bake, remove batter from fridge and allow to come to room temperature. Place the flexipat Canelé tray on a perforated baking sheet and set aside.
Preheat oven to 450°F degrees.
Fill each well of the tray 3/4 full. Bake for 30 minutes. Reduce the oven temperature to 400 degrees Fahrenheit for an additional 30-40 minutes. Allow to cool for 10-20 minutes before removing from tray. Place on cooling rack and allow to cool to room temperature. Serve and enjoy!