Bring the milk and butter to the boil together in a saucepan. Stir the flour and sugar together in a bowl. Beat the egg and yolk together in a cup, and then stir it into the flour mixture. Next, add the hot milk mixture, whisking until smooth. The batter should be thin and lump-free, like crepe batter. Stir in the vanilla and rum. Cover the batter with plastic wrap, and let it sit in the refrigerator for several hours or overnight.
Preheat the oven to 450 degrees F.
Pour the batter into the mini cannele mold, and bake the canneles 15 minutes. Reduce the oven temperature to 350 degrees F, and continue baking until the canneles are dark brown, about 45 minutes to an hour. The cakes are meant to be quite dark on the outside. Unmold the cakes, and cool before serving.