Preheat oven to 400 degrees F. Coat a donut pan with nonstick spray.
In a large bowl, combine flour, baking powder, pumpkin pie spice, salt and baking soda.
In the bowl of an electric mixer fitted with the paddle attachment, beat butter and sugar on medium-high until well combined, about 1-2 minutes.
Beat in eggs, one at a time, until well combined.
Beat in pumpkin and vanilla until just combined.
Gradually add flour mixture to sugar mixture at low speed, beating just until incorporated.
Pipe the batter evenly into the donut pan, filling each cavity two-thirds full.
Place into oven and bake for 10-12 minutes, or until donuts are slightly browned and spring back when touched.
For the maple glaze
In a small saucepan over medium heat, heat maple syrup until reduced to 1/2 cup, about 5 minutes. Whisk in butter, vanilla and salt until the butter has melted.
Whisk in confectioners' sugar until smooth.
When the donuts are done, cool for 10 minutes and dip the tops into the glaze. Allow glaze to set on a wire rack before serving.
Serve warm or at room temperature.
Notes
Use 100% pure pumpkin puree. Canned pumpkin puree and pumpkin pie filling are not the same, and are not interchangeable. Pumpkin pie filling comes pre-mixed with sweeteners and spices.
Pipe the batter. Spooning the batter can be difficult and messy. Use a piping bag or Ziploc bag with the corner snipped off to easily pipe the batter into the donut pan.
Avoid overcooking the donuts. Check the donuts around the 8 minute mark. Overbaked donuts will be dry.
Glaze while warm. Dip the donuts in the maple glaze while they are still warm - this will melt the sugar slightly, creating an even coating into a classic, glossy, shiny shell as it cools.
Freeze without the glaze. Let the donuts cool completely, then wrap each donut tightly in plastic wrap before transferring to an airtight, resealable freezer bag. Label, date, and freeze up to 2 months.
Thaw, warm, and glaze. To reheat the donuts from frozen, thaw 1-2 hours at room temperature, then warm in a microwave for 15-30 seconds, glazing the donuts while they are still warm.