Preheat the oven to 350 degrees. Spray two doughnut pans with nonstick cooking spray.
In a medium mixing bowl combine the all-purpose flour, pumpkin pie spice, baking powder, baking soda, and kosher salt. In a large bowl whisk together the brown sugar, unsalted butter, buttermilk, egg, egg yolk, pumpkin puree, and vanilla extract. Next, add the dry ingredients to the wet ingredients and stir until just combined.
Spoon the batter into each doughnut cup filling approximately 2⁄3 full. Bake the doughnuts for about 15 to 16 minutes. Remove from the oven and allow to cool completely on a wire rack.
Once the doughnuts have cooled, spread the maple frosting on top of each doughnut and garnish with pecans.
For the maple frosting: Using a hand mixer, beat the butter until smooth in a large mixing bowl. Next, add in the powdered sugar and mix until combined. Add in the maple syrup and continue to mix until smooth. If you need to add more maple syrup that's okay! Keep adding until desired consistency is reached.