Prepare the pre-dough:
In a large mixing bowl, combine 1 cup of the flour with sugar and yeast. Warm the milk slightly (about 100°F/37°C) and add it to the mixture. Stir well, cover with a cloth, and let it ferment in a warm place for about 30-45 minutes until bubbly and risen.

Make the dough:
Once the pre-dough is ready, add the remaining flour along with lemon zest, sugar, milk, egg, egg yolks, butter, salt, rum, vinegar, and vanilla extract. Mix thoroughly until a soft, elastic dough forms. Knead on a floured surface for about 10 minutes.

First rise:
Place the dough in a lightly greased bowl, cover, and let rise for about 1.5 to 2 hours until it doubles in size.

Shape the doughnuts:
Punch down the dough gently and roll it out to about ½ inch thickness on a floured surface. Using a round cutter (about 3 inches diameter), cut out circles. Place them on parchment paper or a floured baking sheet, cover, and let rise for another 30 minutes.

Heat the oil:
In a deep heavy pot or fryer, heat your oil, lard, or clarified butter to 350°F (175°C). Use a thermometer for accuracy.

Fry the doughnuts:
Carefully place the doughnuts into the hot oil, a few at a time. Fry for 2-3 minutes on each side, turning gently until golden brown. Avoid overcrowding to keep oil temperature steady.

Drain and coat:
Remove doughnuts with a slotted spoon and drain on paper towels. While still warm, roll the doughnuts in granulated sugar until fully coated.

Fill the doughnuts:
Using a piping bag fitted with a small round tip, fill the doughnuts with your favorite jam or hazelnut spread.

Optional decoration:
Dust with powdered sugar before serving for a classic finish.