Position a rack in the middle of the oven. Preheat the oven to 325° F. Line two baking sheets with parchment paper.

Put 2/3 cup (4 ounces) of the chocolate chips in a heatproof container or the top of a double boiler and place it over, but not touching, a saucepan of barely simmering water (or the bottom of the double boiler). Stir the chocolate chips until melted and smooth. Remove from the water and set aside.

Sift the flour, cocoa powder, baking soda, and salt into a medium bowl and set aside. In a large bowl, using an electric mixer on medium speed, beat the butter, brown sugar, and granulated sugar until smoothly blended, about 1 minute. Stop the mixer and scrape the sides of the bowl as needed during mixing. On low speed, mix in the melted chocolate chips until blended. Add the egg and vanilla, mixing until blended, about 1 minute. Add the flour mixture, mixing just until it is incorporated. Mix in the remaining 2 cups chocolate chips.

Using an ice cream scoop or measuring cup with a ¼-cup capacity, scoop mounds of dough onto the prepared baking sheets, spacing the cookies 3 inches apart.

Bake the cookies one sheet at a time until they crack slightly on top and a toothpick inserted in the center of a cookie Comes out with moist crumbs, not wet batter, about 18 minutes, (If the toothpick penetrates a chocolate chip, test another spot.) Cool the cookies on the baking sheets for 5 minutes, then use a wide metal spatula to transfer them to a wire rack to cool completely. The outsides of the cookies will become crisp as the cookies cool.

The cookies can be stored in a tightly covered container at room temperature for up to 4 days.