This is remarkably similar to a crêpe batter. It needs to be made one day ahead and refrigerated overnight to allow the air bubbles to rise out of it. You need special fluted molds to make cannelés, economical silicone versions can be had from online baking equipment suppliers.
16 ounces (2 cups) whole milk
1 ounce (2 tablespoons) butter
3 egg yolks
1 egg white
8.75 ounces (1 1/4 cups) sugar
4.5 ounces (1 cup) cake flour
1 teaspoons vanilla extract
1 tablespoon rum
Combine half the milk and the butter in a small saucepan and bring it to a full boil. Turn off the heat and set the mixture aside. Next, in a medium bowl, whisk together the egg yolks, the white and the sugar. Whisk in the flour, then the remaining cup of milk.
Once all that is combined, steadily whisk in the warm milk-butter mixture. Pass the mixture through a fine mesh sieve, then refrigerate it for at least 24 hours, up to 48.
When you’re ready to bake, preheat your oven to 400 degrees Fahrenheit. Lightly butter your cannelé molds, and fetch the batter container from the fridge. Very lightly whisk it if it has separated. Fill the molds to the top (technique to follow) and bake for 1 hour, rotate the pan and bake another hour until they are very dark. Cool, unmold and eat.