In a microwave-safe bowl, add in the milk and butter.Microwave for 1 minute. If you have a thermometer, check to make sure it's at 110 degrees.
Add in the yeast and give it a stir.
Measure out the sugar and sprinkle about 2 teaspoons of the sugar into the milk and butter mixture. This will feed the yeast. Let it sit for about 5 to 10 minutes to let the yeast proof. It will become foamy.
Meanwhile, in a large glass mixing bowl, add in the remaining sugar and flour. Stir to combine.
Push the flour and sugar to the outside of the bowl and leave a well in the center.
Add the foamy yeast and milk mixture, egg and vanilla bean paste. Stir to combine the liquids in the center without incorporating the well.
Using a spatula, stir the flour into the wet ingredients until combined. It will still be sticky.
On a clean work surface, add 2 T. of flour. I worked on a piece of parchment paper. Knead the dough about 10 times to get the flour incorporated and reduce the stickiness.
Spray the glass bowl with non-stick cooking spray or add 1 T. of vegetable oil. Place the dough in and spray the top with non-stick cooking spray. If you used the vegetable oil, roll the dough into the oil so the top is covered in the oil as well as the bottom.
Cover with plastic wrap or a tea towel and place in a warm area. Let it rise until doubled in size. It took mine about two hours.
Once the dough is doubled in size, add 2 T. of flour onto the clean surface. Roll the dough out onto the flour and place some of the flour on top of the dough. Press the dough to be about ½ inch thick. I just used my hands.
Cut out donuts using a 3 inch circle cookie cutter. Place on a baking sheet with a piece of parchment paper sprayed with non-stick cooking spray. Space them out so they don't touch when they rise.
Place the donuts in a warm place to rise and cover loosely with plastic wrap. Mine took about 1 hour to rise.
While the donuts are rising, add about 2 to 3 cups of vegetable oil into a heavy-bottom saucepan. Using a candy thermometer, let the oil come up to 350 degrees.
Place the donuts two at a time into the hot oil. Adding too many donuts will drop the temperature and give you oily donuts. Let it cook about 2 minutes and flip. Let cook for another 1 to 2 minutes and place onto a plate lined with paper towels.