Italian doughnuts with custard (Bomboloni)

Bomboloni is an incredibly delicious Italian recipe, an irresistible, round, custard-filled treat.

Ingredients
For the dough
290 g flour type 45 or 00 for pizza
30 g powdered sugar
1 egg and 1 egg yolk (total 75 g)
90 ml of whole milk
4 g dry yeast (or 12 g fresh baking powder)
20 g soft butter
5 g salt
zest of one organic lemon
For the pastry cream
250 ml whole milk
2 egg yolks or 1 whole egg
50 g white or pure cane sugar
1/2 vanilla pod
1 teaspoon of vanilla sugar
30 g cornstarch (maïzena)
30 g of butter
For the finishing touch
Sunflower or peanut frying oil
1 bowl of white or cane sugar
1 teaspoon of cinnamon or vanilla
Preparation
Preparation of the doughnut dough: Prepare a leaven or poolish; in a bowl, add 100 g of flour (extracted from the total), the baking powder and a tablespoon of sugar. Mix well, add 90 ml of slightly warm milk at room temperature and mix until it is homogeneous, cover the bowl with cling film and let it rise for about 30 minutes in a warm place.
After this time of fermentation, add the leavening previously prepared in the bowl of the mixer, the eggs beaten with a fork, the sugar, the remaining flour, the grated lemon peel or vanilla and the softened butter and start kneading with the hook for about 10 minutes.
The ingredients should mix and combine to form a homogeneous dough that is a little sticky but can be removed from the bowl of the food processor. If the dough is very sticky, gradually add flour by teaspoonfuls until you reach the desired consistency, which is very similar to a smooth brioche dough.
Form a dough, place it in a bowl, cover it with cling film and leave it to rest in a warm place for about an hour and a half to two hours depending on the room temperature.
In the meantime, prepare the pastry cream: In a saucepan, pour the milk and half the sugar (25 g). Scrape the vanilla bean with a knife and add the seeds of half a bean and the stem to the milk.
Bring the mixture to a boil over low heat to infuse the vanilla into the milk.
In a bowl, place the whole egg or both yolks with the remaining sugar (25 g) and vanilla sugar and beat vigorously with a whisk until the mixture turns white and the sugar crystals are dissolved.
Gradually add cornstarch (cornstarch type) or, if not available, flour to the egg and sugar mixture. Mix gently so as not to form lumps.
Once the mixture is homogeneous, pour half of the vanilla flavored milk – just boiling – on the cream mixture. Mix gently at first and then more vigorously to loosen the cream. When the cream is soft, pour it back into the pan with the remaining half of the milk.
Return the pan to low heat. Stir constantly until the first bubbles appear, which coincides with the thickening of the cream. The cream should remain soft.
Finally, when the cream is sufficiently cooked, turn off the heat and stir in the butter, then continue to whip it to cool more quickly.
To prevent a dry crust from forming on the surface, cover it with cling film and keep it in a cool place.
When you are ready to use it, remove the vanilla bean and whisk it once more to obtain a light consistency!
Shaping and cooking the doughnuts: Once the doughnut dough has risen, divide it into 12 equal sized balls and roll them on a clean work surface without flour.
Let the doughnuts rise for about 40 minutes to 1 hour in a warm, draft-free place. Heat a generous amount of sunflower or peanut oil in a heavy-bottomed saucepan or skillet. The oil temperature should not be too low, otherwise the fritters will absorb too much oil, nor too high, otherwise they will be too colored on the outside and raw on the inside.
Fry the doughnuts by turning them over when they are cooked, then place them on absorbent paper.
Coat the doughnuts in sugar mixed with cinnamon and then fill them with custard using a pastry bag fitted with a small tip. Cut a small hole in the side of each doughnut and pipe about a tablespoon of custard into each doughnut.