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.
Scoop the batter evenly into the donut pan. Place into oven and bake for 10-12 minutes, or until donuts are slightly browned and spring back when touched.
To make the glaze, heat maple syrup in a small saucepan over medium heat 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 before serving.