Whisk together flour, cocoa, baking powder, spices, and salt.
In work bowl of a stand mixer outfitted with flat beater blade, beat butter and both sugars on medium speed until very light and fluffy, at least 5 minutes. Scrape down bowl and beater with rubber spatula.
Add egg and vanilla and beat on medium until incorporated.
Turn speed down to low and add flour mixture a spoonful at a time. Mix just until combined.
Divide dough in two equal pieces. Form each piece into a log 1-1/2" across. Wrap tightly in plastic wrap and refrigerate at least 2 hours, or up to 3 days. (You can freeze up to 1 month - just thaw in refrigerator overnight before continuing.).
Preheat oven to 350F and place racks in upper middle and lower middle positions.
Slice logs 1/4" thick. Place discs 1/2" apart on 2 baking sheets - you should get about 20 cookies on each sheet.
Bake 6 minutes. Rotate each sheet back-to-front, and swap racks top-to-bottom. Bake another 6-7 minutes, until edges are firm but centers are still soft.
Place sheets on wire racks and cool 5 minutes, then transfer cookies to racks to cool complete. Store in an airtight container at room temperature, up to 3 days.