In a medium bowl, whisk together flour, cocoa powder, and baking soda. Set aside.
In a large bowl, cream together butter, peanut butter, granulated sugar, and brown sugar until light and fluffy.
Beat in the egg and vanilla extract until well combined.
Gradually blend in the dry ingredients until just mixed.
Drop rounded tablespoonfuls of dough onto ungreased baking sheets.
Bake in preheated oven for 10 minutes, or until edges are set. Cool on baking sheets for 2 minutes before transferring to wire racks to cool completely.
Notes
Store cookies in an airtight container for up to a week.