For the doughnuts:

1. Brown the butter by cutting it into 1 tablespoon cubes and heating them in a skillet on medium heat. Add the 1/4 cup bourbon and cook until the butter takes on a light brown color and little brown bits start to form about 5-10 minutes. Remove from heat and let it cool.
2. Heat the milk until it’s lukewarm, about 90 degrees. You need it warm enough to activate the yeast, but if it’s too hot it will kill the yeast.
3. In a bowl fitted to a stand mixer fitted with a dough hook, combine the yeast and the milk. Let it sit until it starts to foam—about 5 minutes.
4. Add in the butter, eggs, sugar, vanilla, and salt and beat until combined. Add in half the flour and mix until combined. Scrape down the sides with a spatula and, in the remaining flour, beat until smooth.
5. Transfer to a greased bowl, cover with plastic wrap, and let rise for 1 hour.
6. Once risen, turn the dough onto a floured surface and roll it out until it’s 1/2 inch thick. Cut out doughnuts with a 3in circle cookie cutter and then cut out the center with a 1in cutter. Place cut out doughnuts on parchment paper with plenty of room inbetween, cover, and let rise again for 45 minutes.
7. About 15 minutes before doughnuts are ready, heat your oil in a large pot until it reaches 375 degrees. When the oil is ready, fry about 3 doughnuts at a time—cooking each side about 30 seconds- 1-minute per side. You are looking for a nice golden brown color.
8. Place on paper towel-lined plates.

For the glaze:

1. Mix the bourbon and powdered sugar in the medium bowl and mix until there are no lumps.
2. Drizzle the glaze around each one of the cooled doughnuts.