Add flour to a bowl and form a well in the middle. Add 1 tablespoon of sugar and the yeast to the bowl and mix with about a quarter of the lukewarm milk while incorporating some of the flour from the rim of the well.

Cover with a clean kitchen towel and set aside for 15 minutes.

In the meantime, whisk the egg and the egg yolks in a small bowl with a fork and melt the butter in the remaining milk.

Cover the well with some flour, then add the eggs, the milk mixture, remaining sugar, rum, and a pinch of salt to the bowl. Knead for about 10 minutes on medium-low speed.

Flatten the balls with the palm of your hand or a small plate to about ½ inch in height and set aside for 30 minutes.

In the meantime, heat oil in a large pot or deep pan to 320 degrees Fahrenheit.

With a slotted spoon, lower the dough pieces into the hot oil. Place a lid on the pot and bake for 3 minutes. Remove the lid, turn the dough balls, and bake uncovered for another 3 minutes.

Remove carefully and place on a plate lined with paper towels. Dust with powdered sugar or roll in caster sugar.