In a medium bowl, combine the flour, baking soda, baking powder, salt, and pumpkin pie spice. Set aside.

In the bowl of a mixer, beat the butter and sugar until light and fluffy. Beat in the eggs, one at a time, scraping down the sides as needed. Add in the vanilla and pumpkin and beat until combined.

Add the flour mixture and mix until combined. Divide the mixture into 2 and wrap each in plastic wrap. Refrigerate for at least 2 hours or preferably overnight.

Preheat the oven to 425ºF. Line baking sheets with parchment paper or silicone liners.

Lightly flour a work surface. Roll the dough to 1/4-inch thickness. The dough will be a little sticky, so use flour as needed to avoid sticking. Use a 2 to 2 1/2 inch round cookie cutter to cut out circles and transfer to the prepared baking sheets. Bake the cookies until just set and still pale, about 7 minutes. Transfer to a cooling rack or piece of waxed paper to cool completely before frosting.

To make the frosting: in a large bowl, beat the butter until soft and fluffy. Add in the maple extract. Add in the powdered sugar, 1/2 cup at a time. Beat until combined completely. Add in the cinnamon and salt and beat, then add the cream and continue to beat until light and fluffy.

Frost each cookie with the frosting and then top with sprinkles, if desired.