Brown the butter in a light-colored saucepan over medium heat, stirring continuously, until milk solids are golden-amber and it smells nutty — 5 to 7 minutes. Pour into a large bowl, scraping all browned bits. Refrigerate 45 minutes (or freeze 15 minutes) until re-solidified to softened-butter consistency.
Beat re-solidified brown butter with both sugars 2 to 3 minutes until fluffy. Add pumpkin puree; beat 1 minute. Add egg yolk and vanilla; beat 30 seconds. Fold in flour, baking soda, baking powder, salt, and spices until no flour streaks remain. Do not overmix.
Cover with plastic wrap pressed to the dough surface. Refrigerate at least 1 hour, overnight for best flavor and texture.
Preheat oven to 375°F (190°C). Scoop 2-tablespoon portions, roll into balls, press lightly to ¾-inch thickness, and place 2 inches apart on parchment-lined sheets. Bake one sheet at a time 11 to 13 minutes. Edges should look set; centers should still look slightly glossy. Cool on pan 5 minutes, then transfer to a wire rack and cool completely.
Whisk glaze ingredients until smooth. Drizzle over fully cooled cookies or dip the top third into the glaze. Let set 20 to 30 minutes before stacking or storing.