In the bowl of a stand mixer or in a large bowl with a hand mixer, beat together butter, pumpkin puree, and sugar until light and fluffy, about 3 minutes.
Beat in egg yolk and vanilla.
In a separate large bowl, whisk together flour, almond flour, cinnamon, ginger, nutmeg, and salt. Add flour mixture to the wet mixture and mix until just combined, taking care not to over-mix.
Divide dough in half and pat each half into a disc. Wrap dough in plastic wrap and place in fridge until firm, about 1 hour.
On a floured surface, sprinkle a dusting of flour over one dough disc (leave second disc of dough in fridge) and roll dough out to be about ¼"-thick. Cut out cookies with a medium or large cookie cutter (2½" is recommended) and transfer to a parchment paper-lined baking sheet.
Be sure to re-roll and dough scraps to cut out as many cookies as you can. Place cookie sheet in fridge for about 30 minutes and take second dough disc out.
Roll second dough disk out to be about ¼"-thick and cut shapes with same cookie cutter. Transfer these to a second parchment paper-lined baking sheet and use your smallest cookie cutter to make a cutout in the center of each. Place this cookie sheet in fridge for 30 minutes to chill.
Preheat oven to 350°F.
Bake both sheets of cookies for 8 to 10 minutes, or until the edges are just beginning to turn golden. Let them cool for 5 minutes on the pan, before transferring to a wire rack to cool completely.
Place the cookies with the holes in them on a cookie sheet and sift confectioners' sugar over the top. Turn the remaining cookies flat side up and spread about 1 teaspoon of pumpkin cinnamon buttercream into the center. Top with the sugar-dusted cookies.