Preheat your oven to 350°F and line baking sheet with parchment paper or a baking mat.
Scoop pumpkin puree onto a very clean dish towel or a couple layers of paper towels, fold towel over the puree, and press down firmly, squeezing moisture out of. Flip the puree onto a dry spot and repeat once or twice more until most of the moisture has been removed and you can pick the puree up in a ball.
Melt butter in a medium, heavy-bottomed, light-colored saucepan over medium heat. Bring to a simmer and cook, swirling the pan frequently, until butter becomes a medium nutty brown color. Do not leave the butter unattended as the milk solids will burn easily. Remove from heat.
Add prepared pumpkin puree to the butter and whisk vigorously until well-combined (it will bubble and pop, so be careful).
In a large bowl, whisk together all of the dry ingredients. Pour pumpkin and butter mixture over the top and use a rubber spatula to stir the ingredients until well-combined.
Place the dough between 2 sheets of parchment paper and roll out to about 1/4-inch thick. Place in the refrigerator while you clean up, about 5 minutes.
Remove dough from the refrigerator and cut out 30 to 40 1 1/2-inch rounds. Use a metal spatula to transfer rounds to prepared baking sheet. Gathering scraps and re-rolling (between your sheets of parchment paper) as necessary.
Bake for 10 to 12 minutes, until the tops of the cookies lose their shiny, under-cooked look.
Cool completely on the tray, at least 20 min.