In a microwave-safe bowl, whisk together the milk and beer.

Microwave the mixture in 10-second intervals until it reaches 105°F.

Pour the beer mixture into the bowl of a stand mixer. Add the yeast and stir to combine. Let it stand for 5 minutes.

Add the sugars, salt, vanilla extract, spices, egg, yolks, and pumpkin puree.

With the dough hook, mix on medium speed for 30 seconds to 1 minute, or until thoroughly combined.

Add the bread and pastry flour and mix on medium-high for 4 to 6 minutes, or until a soft, sticky dough forms.

Transfer the dough to a buttered bowl. Cover with plastic wrap and let it sit on the counter for about 1 hour, or until the dough has doubled in size.

Scrape the dough out of the bowl onto a floured surface. Flour your hands to make handling the sticky dough easier.

Knead for about 1 minute, punching it down and adding a bit more flour if it becomes too sticky.

Line baking sheets with parchment paper.

Using a floured rolling pin, roll out the dough to about 1/2 inch thick.

Cut out donut rounds with a floured 3-inch cutter. Arrange them on the prepared baking sheets, leaving 2 inches between each donut.

Re-roll the dough scraps and cut out more donuts until all the dough is used.

Punch out the center of each donut with a floured cutter, between 1/2 and 1 inch in diameter. Transfer the donut holes to another lined baking sheet.

Cover the baking sheets with plastic wrap and let the donuts rise in a warm spot for 1 hour up to 1 hour and 30 minutes.

Preheat the oven to 400°F.

Bake the 3-inch round donuts for 20 minutes, or until light golden brown. You can bake the donut holes for 10 minutes, or until golden.

Heat a saucepan over medium heat.

Add the butter, stirring frequently to help it melt.

The butter will crackle and bubble up. Eventually, the foam will disappear. Continue whisking.

Once the butter turns amber brown and smells nutty, remove it from the heat and transfer it to a heatproof bowl. Let it cool before use.

Dip each baked pumpkin donut and donut hole into the melted brown butter, then coat with cinnamon sugar.