Dissolve the yeast in a bowl with the warm water and 1 teaspoon sugar, stirring until completely dissolved. Set aside for a few minutes while you prep the rest of the ingredients. You want it to start to form a foam on top to make sure that the yeast is active.
½ cup water, 1 teaspoon sugar, 1 packet active dry yeast 7g
Combine flour, brown sugar, pumpkin spice, and salt in a large bowl and mix. Make a well in the middle and add butter, eggs, vanilla, pumpkin puree, milk, and the yeast mixture.
½ cup unsalted butter, 5 cups all purpose flour 600 g, ¼ cup brown sugar, ½ tablespoon pumpkin spice, ⅛ teaspoon salt, ¼ cup butter, 2 large eggs, 1 teaspoon pure vanilla extract, ¾ cup canned pumpkin puree, ¼ cup milk
Use a spoon to mix at first and then get in with your hands to mix until a sticky and shaggy dough forms. If not all of the butter gets mixed into it, it's ok.
Cover with a cloth and let rise in a warm place (see notes) until doubled in size, about 30- 45 mins.
Turn out the dough onto a well floured surface and flatten and fold a few times with your hands to give it a good mix. Roll out to ¾" thick. Cut out about eighteen 3.5" circles of dough and transfer onto a parchment lined baking sheet, rerolling the dough as needed. Let the dough rise in a warm place until doubled, about 15 minutes. Save the dough scraps.
While the dough is rising, heat the oil in a large heavy bottom pot (I used a wide and narrow pot). Clip a cooking thermometer onto the side of the pot to monitor the temperature. Heat to 190°C (370°F).
100 oz vegetable oil
Prepare a baking tray lined with 4 layers of paper towels for the freshly fried donuts. Prepare a cooling rack with a layer of paper towels underneath as well. Mix together the sugar and pumpkin spice in a large bowl for the sugar topping.
1 cup granulated sugar, 1 teaspoon pumpkin spice
When the oil comes to temperature, add the dough scraps. Fry on each side for 2-3 minutes or until golden brown. Remove from oil with tongs or a spider. Gently shake excess oil off and transfer onto paper towels. Blot them with paper towels and transfer onto cooling rack.
Repeat with the rest of the dough, making sure that the oil temperature stays at 190°C (370°F) and do not overcrowd the pan.
Once donuts are cool enough to handle, coat in sugar mix and coat well. Set aside to cool completely.
Once the donuts are completely cool, poke a hole through one side with a chopstick or knife.
Fill a piping bag fitted with a piping tip with the cooled pumpkin custard filling. Fill the donuts through the hole until they feel heavy and the filling starts to come out. Enjoy!