Whisk 1½ cups of the flour with ¼ cup sugar, the salt and yeast, in a bowl.

Stir in the milk and then 3 tablespoons of the oil, along with the white rum, vanilla, egg yolks, and oil.

Beat for 2 minutes with an electric mixer.

Stir in more flour if needed (up to ¼ cup more) to get the dough to stick together.

Now turn the dough on to a floured surface and knead for 5 minutes.

Use plastic wrap to cover, then let it sit for 10 minutes.

Meanwhile, make the filling.

Put the sugar and cornstarch in a pan over a moderate heat.

Stir in the milk and egg gradually.

Bring the mixture to a boil, stirring all the time.

Cook for about a minute or until thick.

Let it cool completely.

Use parchment paper to line a baking sheet.

Roll the dough into a disk that’s ½-inch thick.

Cut out 2½ rounds with a flour-dipped cookie cutter.

Roll any scraps back up and cut more rounds from that.

Put the rounds on the baking sheet.

Cover with a clean towel and leave for an hour.

Heat canola oil to 360°F in a deep fryer or large, heavy pot.

Drop the dough in, using a metal strainer or heatproof utensil.

Cook about 3 at once time, flipping them when dark brown on one side.

When the other side is also dark brown, drain on a wire rack.

Put a long, thin tip on a piping bag and fill with the refrigerated custard mixture.

Pipe the filling into the rounds, then brush melted butter on both sides.

Dip in sugar, then serve right away.