Place most of the milk on the stove, reserving a few tablespoons. If using a vanilla bean, split it and add it to the milk when heating.
Separately, whisk together the sugar, egg yolks, the remaining milk, cornstarch, and a pinch of salt. When the milk begins to boil, slowly pour it over the egg yolk mixture, stirring vigorously.
Pour the vanilla cream mixture back into the saucepan and cook over medium heat until it thickens, stirring regularly. Once the vanilla cream is ready, melt the butter into it and add the vanilla extract if you’re not using a vanilla bean. Cover it with plastic wrap and let it cool.
Combine the sugar and warm milk, then add the dry yeast. Let it sit for 10-15 minutes until it becomes frothy. Separately, mix the flour and salt, then combine it with the yeast mixture along with the eggs. Knead until you have a smooth dough, about 10 minutes.
Incorporate the soft butter, kneading for another 15 minutes or until the dough becomes fluffy and elastic. Let the donut dough rise until it doubles in size (at least 1 hour).
Roll out the dough on a floured surface to a thickness of 1 cm. Cut out donut shapes using a cutter or a wide glass. Let the donuts rise for at least 30 minutes.
Fry the donuts over medium heat, 2-3 at a time, until they turn golden brown on both sides. Roll the fried donuts in powdered sugar or fine sugar. Fill the donuts with the prepared vanilla cream using a pastry bag with a simple tip.