Preheat oven to 350°F (175°C). Line baking sheets with parchment paper or silicone liners.
Whisk together the flour, cocoa powder, baking soda, and salt. Set aside.
Using an electric mixer on medium speed, beat the butter, sugar, and brown sugar until light and fluffy. Add the egg and vanilla, and mix well.
Reduce the mixer speed to low. Gradually add the flour mixture, mixing just until combined. Stir in the chocolate.
Scoop the dough by teaspoonfuls and roll each portion into a ball. Place 2 inches apart on prepared pans. Flatten the top of each cookie slightly. Sprinkle with sea salt.
Bake the cookies, one pan at a time, for 7 to 9 minutes, or until the edges are set but the centers are still soft. Cool on the pans for about 5 minutes. Then transfer the cookies to a wire rack to cool completely.
Notes
If your kitchen is warm, consider chilling the dough for about an hour to help keep them from spreading too much as they bake.