In a large bowl with an electric handheld mixer (or in the bowl of a stand mixer fitted with the paddle attachment), cream together the butter, brown sugar, and granulated sugar until light and fluffy, 1-2 minutes.
Add the eggs and vanilla. Mix until the batter has lightened in color, 2-3 minutes.
In a separate bowl, whisk together the flour, cocoa powder, baking soda, and salt (or sift these ingredients right into the bowl with the cookie batter). Mix until evenly combined.
Refrigerate the dough for at least 30 minutes but preferably an hour (and up to overnight). If refrigerating the dough overnight, consider scooping the soft dough into cookie dough portions before refrigerating as it will make it much easier to scoop than waiting until the dough has chilled/set up more.
Preheat the oven to 350 degrees F. Line two, large baking sheets with parchment paper. Set aside.
Place the powdered sugar in a bowl or shallow dish. If you haven't already, scoop the dough into heaping tablespoon-sized balls (I use a #40 cookie scoop) and roll into a smooth ball shape.
Roll each ball in the powdered sugar and place several inches apart on the baking sheets.
Bake for 10-11 minutes until puffed and crackled on top. Remove from the oven. Let the cookies rest a few minutes on the baking pan before removing to a cooling rack to cool completely.
Notes
Chilling: the chilling time is really important for this recipe so the cookies don't spread or flatten too much while baking. Speaking of chilling, the baked and cooled cookies are exceptionally delicious if stored in the refrigerator and eaten cold. Flat Cookies: if your cookies are baking up more flat than you'd like try increasing the oven temperature by 25 degrees and/or adding 1/4 cup (more or less) additional flour to the cookie dough.