Add milk to the stand mixer bowl and sprinkle yeast on top. Allow it to activate for 5 minutes before mixing it with the other ingredients. Whisk together the sugar, oil, egg, and vanilla extract.
Slowly add the flour, butter, and pinch of salt into the mixture. Mix the dough on speed 2 of the stand-mixer until everything is well combined. Knead the dough for about 7 minutes, or until it is smooth and elastic.
On a clean work surface, knead the dough several times and shape it into a ball. Place it into a lightly greased bowl and roll the dough around to lightly coat it with the oil. Cover with plastic wrap and leave it aside at room temperature for about 2 to 3 hours until the size has tripled.
Knead the dough a couple of times and roll it out to � - ? inch thick and cut about 6 rounds of dough out with a cookie cutter.
Place the cut dough on a lined baking sheet, then cover with plastic wrap and leave it to rise for about 1 hour.
Fill a pot with vegetable oil and heat to 170�C to 175�C. Drop the doughnuts in carefully and start frying. Turn them a few times and cook for 2 to 3 minutes on each side, or until golden brown.
Remove the fried doughnuts and transfer them to a plate lined with a paper towel. Then, roll them immediately in a bowl of sugar. Make sure to coat the entire doughnut.
Let the doughnuts cool a little before making an indentation at the side using a wooden spoon. Fill the doughnut with a pastry cream or any filling of your choice using a piping bag, serve and enjoy!