Preheat oven to 350 degrees. Line 2 baking sheets with parchment paper. In a medium bowl, whisk together flour, cocoa powder, baking powder, and salt. Set aside.
In a standing mixer fit with the paddle attachment on medium speed, or with an electric hand mixer, beat sugar and butter until pale and fluffy, about 3 to 4 minutes. Scrape down the sides of bowl as necessary.
Add eggs and beat well. Beat in red food coloring, vinegar, and vanilla extract. Gradually add the flour mixture. Scrape down the sides of bowl as necessary.
Working with 1 heaping tablespoon of dough at a time, roll dough into 1 1/2-inch balls and lay on prepared baking sheets about 2 inches apart. (I use the OXO medium cookie scoop, a size 40 portioner, and do 12 scoops of dough per baking sheet).
Bake until the edges are golden brown, about 10 to 12 minutes. Cool on pans 5 minutes, then cool completely on wire racks. Repeat with remaining cookie dough (Yield: about 48 cookies).