In the bowl of a stand mixer, cream the butter and powdered sugar together until fluffy and well combined. Add the pumpkin puree, pumpkin pie spice, extract, and salt. Let them get thoroughly mixed in. Turn the speed to low and gradually add in the flour just until it disappears. Lay out a big sheet of plastic wrap and turn the dough out onto it. Gently form the dough into a long log across the length of the plastic wrap, then roll it up in the wrapping. Gently roll it back and forth to help it get longer and more round. Let the wrapped dough sit and harden in the refrigerator overnight if possible, or at least 3-4 hours.

Once the dough is done refrigerating, preheat the oven to 325 and line a baking sheet with a silicone mat or parchment paper. Take the dough out and slice it into little roughly 1/2 inch thick rounds with a sharp knife. There should be about 28. Just make sure there is an even number to make sandwiches! Since they don't spread much while baking, all 28 should line up beautifully on the sheet tray.

Bake the shortbread cookies for about 20 minutes, until set and golden. Let them cool for 5-10 minutes, then carefully transfer them to a rack to finish cooling. Then it's time to assemble the sandwiches! Spread a heaping spoonful or two of the pumpkin spiced cookie butter on the bottom of one cookie. Close the sandwich with another cookie, facing the bottom side down. Repeat until all of the sandwiches are made. Serve immediately and enjoy!