In a small bowl place the milk and stir in the yeast, then let it sit for 15 minutes for the yeast to rise and activate.
In a different big bowl, mix together the flour, sugar and salt. Add in the yeast mixture, the egg and the butter. Start mixing by using your hands or a wooden spoon until you form a dough ball.
Place this dough on a clean surface and knead for 20 min. until it is soft and elastic (all of the previous kneading process could also be done in a standing mixer with the dough hook attached).
Form a ball with the dough, and coat with some vegetable oil and place it in a bowl, then cover this with plastic kitchen wrap or a kitchen towel. Let it rest for 1 hour or until it doubles in size.
Once the dough has doubled in size, place it on a clean surface with some flour and roll it our using a rolling pin until about 1/2 inch (1cm) thick.
Cut 10 circles out of this dough, using a cookie cutter. Place these circles on a previously greased baking sheet and cover them with eome plastic kitchen wrap or a kitchen towel. Let them rest for 30 min. or until they double in size again.
In a medium size pot, heat enough oil for frying. Once the oil is hot (you can test it by dropping a amall piece of dough before frying the donuts) fry the donuts a few pieces at a time until golden and fully cooked.
For the cream filling:
With a sharp knife, open in half the vanilla bean, and take out all of the seeds.
In small pot, place the milk along with half the sugar and the vanilla bean seeds and cook it to low heat, mixing ocasionally with a whisk.
In a small bowl, mix the rest of the sugar along with the salt, egg yolks and cornstarch. Add in some of the milk mixture and mix for the egg yolk mixture to temper.
Pour the egg yolk mixture into the milk pot, and keep on cooking now beating non stop, until the mixture thickens.
Take this out of the heat and mix in the butter while still hot. Pour this into a different bowl and cover with some plastic wrap (which must touch the surface of the cream, so that a custard does not form on top and refrigerate for 1 hour.
For the chocolate glaze:
For the chocolate glaze, place the chocolate in a small bowl and set aside. Place the whipping cream in a small pot and cook to medium heat for 1 minute bringing it to a boil.
Pour this cream over the chocolate and let it sit for 1 minute, then mix until a light ganache forms.
To assemble:
To fill the donuts, make a hole on the side of them using a wooden toothpick and using a pastry pipping bag fill them.
Glaze them with the chocolate and let them sit for 10 min. before eating.