Sift together flour, cocoa, and salt into a bowl.
Place butter in the bowl of an electric mixer fitted with the paddle attachment. Beat on medium speed until fluffy, about 5 minutes. Add sugar, and beat about 2 minutes more, until very light in color and fluffy, occasionally scraping down the sides of the bowl with a spatula. Add vanilla, if using. Add flour mixture, and combine on low speed, scraping with spatula if necessary, until flour is just incorporated and dough sticks together when squeezed with fingers. Form dough into a flattened disk; wrap in plastic. Chill until firm, at least 1 hour.
Preheat oven to 325 degrees. Line two baking sheets with parchment paper.
Using a spoon, form dough into 1-inch balls; place on prepared baking sheet. Bake until firm, 20 to 25 minutes, rotating halfway through. Cool completely on wire rack. Dust with cocoa powder just before serving.
Cookies can be stored in an airtight container at room temperature up to 1 week.