Brown butter. Melt butter in a small pot or pan over medium-low heat until it starts to brown.
Whisk dry ingredients in a bowl. In a separate large bowl or stand of an electric mixer, combine cooled brown butter, egg, vanilla, and pumpkin puree.
Beat on low. Combine wet ingredients with dry ingredients and mix until a soft dough has formed. The batter will be more on the moist side (not sticky dough). Chill the dough in the fridge for at least 1 hour or in the freezer for 30 minutes.
Take about 2 heaping tablespoons of dough, roll into balls, and place on large baking sheets lined with parchment paper. Gently press on each dough ball to flatten it.
Bake at 350 F for 10-12 minutes. Cookies will have a soft center and look underbaked. They are ready to be taken out of the oven!
Let the cookies cool in the pan before transferring to a wire rack to cool off completely.