Line a 12-by-17-inch baking sheet with parchment paper.
Into a medium bowl, sift together the flour, cocoa powder, baking soda and salt.
In the bowl of a stand mixer fitted with the paddle attachment, beat the butter on medium speed until creamy. Add 2/3 cup of the sugar and beat until light in color and texture, about 3 minutes. Add the egg and vanilla extract and beat until the egg is fully absorbed and the mixture lightens in color, 1 minute more. Reduce the speed to low and gradually stir in the flour mixture just until combined (avoid over-mixing or the cookies will be dry!). Stir in the chocolate.
Use a 1 tablespoon measuring spoon to portion the dough onto the prepared baking sheets- 12 cookies per sheet, evenly spaced (the cookies won't spread too much during baking). Freeze until the dough is solid, about 30 minutes.
Meanwhile, position a rack to the center of the oven and preheat the oven to 350 degrees F.
Roll the dough balls in the remaining 1/3 cup sugar to coat completely.
Bake the cookies just until they are slightly puffed and the edges can be lifted off the parchment with a fingertip, but the cookies look somewhat underdone and soft towards the center, 10 minutes, being careful not to over-bake. Cool the cookies completely on the baking sheet set over a wire rack. Store in an airtight container at room temperature for up to 5 days.
Store the frozen dough balls in a resealable plastic bag in the freezer for up to 6 months. To bake from frozen, add about 1 minute onto the baking time.