Position your oven racks in the top and lower thirds of your oven.
Preheat oven to 400F.
Line two cookie sheets with parchment paper or with Silpat.
Whisk together the flour, baking powder and baking soda. Set aside.
Beat the butter, sugar, salt, vanilla, espresso powder and spices until light and fluffy, scraping bowl as necessary.
Beat in the egg until completely incorporated.
Beat in the pumpkin puree.
On low speed, beat in the flour mixture until just combined, scraping bowl as necessary.
Finish mixing by hand, if necessary.
Scoop out cookies in generous 2 tablespoon portions onto prepared sheets, six per sheet. Flatten the mounds of dough a bit with the back of a spoon or with a spatula.
Bake for 5 minutes. Rotate your cookie sheets, and bake for 5 minutes more, or until the cookies are firm on top and spring back a bit when touched. Don't let them brown.
Remove to cooling racks.
Whisk all glaze ingredients together, adding as much milk as necessary to make a nice thick-ish glaze consistency.
Top each cookie with as much glaze as you want, letting it run where it will.
