Whisk together flour, cocoa, baking soda, and salt in a medium bowl.
Beat together butter and sugar with an electric mixer until pale and fluffy, then beat in eggs and vanilla until combined. Add flour mixture and mix just until combined.
Drop level tablespoons of dough about 2 inches apart onto ungreased baking sheets and bake in batches in middle of oven until puffed and set, about 12 minutes. Transfer cookies to a rack to cool.