Preheat oven to 375. Whisk together flour, cocoa powder, baking powder, and salt in a medium bowl; set aside.
Put butter and sugar into the bowl of an electric mixer fitted with the paddle attachment. Mix on medium-high speed until pale and fluffy. Mix in shortening (or additional butter). Add egg and vanilla; mix until creamy. Reduce speed to low. Gradually add flour mixture, and mix until just combined.
Using a 2 1/2-inch ice cream scoop, drop dough onto baking sheets lined with parchment paper, spacing about 4 inches apart. Bake until edges are firm, 18 to 20 minutes. Let cool on sheets on wire racks. Cookies can be stored in an airtight container up to 2 days.