Only use a hand blender with thick stirrers.
1. Pour the flour in a bowl, make a well with your fingers and place the yeast, warm milk and sprinkle with some sugar. With a fork, stir only the part inside the well until you form a sludge. Leave the rest of the flour aside. Sprinkle with a little flour on top, cover it and put it in a preheated 86°F (30 °C) oven that you've turned off, for about 15-20 min.
2. In a bowl, put the yolks and the whole egg with the rest of the sugar. Use the hand blender to beat until whitened. Add the lemon zest, rum and the rest of the milk, while stirring with a whisk.
3. Take the ready dough out of the oven and add the egg mixture to it, with the blender on low speed. Add salt and the melted cool butter. Beat for about 10-15 min. with the stirrers. Form a ball of dough, take it out and place it in a lightly buttered bowl, sprinkle with flour, wrap with a towel and leave it to rest for about 20 min.
4. Sprinkle the counter well with flour, place the dough onto it and knead it by hand for a few min. until it becomes a nice and stretchy ball. Don't knead long. Put it in the lightly buttered bowl again, sprinkle with flour and leave it to rise for about 1 1/2 hours.
5. Sprinkle flour through a sieve onto a large, flat tray, distributing it everywhere.
6. Place the ready dough onto the floured counter, knead lightly and roll it out into a 1/8" thick sheet. Cut out circles about 2 3/4″ (7 cm) in diameter, place them in the floured tray. Gather up the rest of the dough, roll it out and cut out circles once again. Cover them with foil and leave to rise again for 30-40 min. Or place them in a preheated 86°F (30 °C) oven that you've turned off.
7. Prepare a deep pot with a thick bottom and pour about 6 1/5 cups oil in it. The temperature needs to reach about 329°F (165 °C), a moderately heated stove. Put the circles in the hot oil and fry on each side about 1-2 min. Take them out, place onto paper towels for the oil to drain away.
Vanilla cream filling:
Add the egg mixture in a thin trickle while stirring nonstop with a whisk. Boil until it thickens. Remove from the fire, cool it for 15 min. and add the diced cubes of butter while stirring nonstop. Cover with foil and let it cool completely.
Spray it into each donut using a long tip.
Source: The recipe is from a German culinary site and YouTube video.
Note: They're every easy to make but the most important thing is frying them in hot oil. Keep an eye on them because they burn very quickly.