• Heat the pumpkin ale in a small saucepan over medium-low heat until it is reduced to 1/4 cup, about 20 - 30 minutes. Set aside to cool.
• Mix the flour, baking soda, baking powder, salt, and pumpkin pie spice together is a medium sized bowl. Set aside.
• In a stand mixer using the paddle attachment, beat the butter and granulated sugar together until smooth.
• Add the eggs, one at a time, and beat until fully incorporated. Use a rubber spatula to occasionally scrap down the sides as necessary.
• Gradually add the reduced pumpkin ale and the buttermilk, mixing just until combined.
• Add the flour mixture, and continue to mix just until dough comes together. It was very sticky.
• Line two baking sheets with parchment paper and generously coat with flour. Turn the dough out onto one of the baking sheets, and press down with your hands until it is about 1/2 inch thick. Use more flour is dough is still wet. Place the dough and baking sheet in the freezer for 20 minutes until slightly hardened.
• Remove from freezer, and cut out 3 inch circles with 1 inch holes in the center.
• Place the cut doughnuts and doughnut holes onto the second baking pan. Re-roll dough scraps and cut out remaining circles. Refrigerate the doughnuts for 20 to 30 minutes.
• Heat 2 to 3 inches of oil in a large deep-sided pan until a candy thermometer reaches 350 degrees. Line a baking sheet with several layers of paper towels and set aside.
• Gently drop a few doughnuts at a time into the hot oil. Do not overcrowd the pan. Fry until golden brown, turn over and fry the other side.
• Remove doughnuts from oil and drain on paper towels.
• Dip the cold doughnuts into the glaze.

To make the Cream Cheese Glaze:

• Beat cream cheese until smooth.
• Add the sugar, maple syrup, and extract. Add the milk to thin to desired consistency.
• Dip cooled doughnuts into glaze and decorate as desired.

To make Pumpkin Spice Glaze:

• Whisk sugar and liqueur together in a small bowl. Dip warm doughnuts into glaze.