Preheat the oven to 350°F. Line one or two baking sheets with parchment paper and set aside.
In a medium bowl, whisk together the flour, salt, baking powder, and baking soda until evenly combined.
In the bowl of a stand mixer or a large mixing bowl, beat the butter, sugar, and sifted cocoa powder on medium speed until well blended, about 2 minutes, scraping the bowl down once or twice.
Add the eggs one at a time, mixing until blended after each addition. Stir in the vanilla.
Add the melted, slightly cooled semisweet chocolate and mix until combined.
Add the flour mixture and mix on low speed (or fold by hand) just until incorporated; avoid overmixing.
Use a tablespoon to drop rounded tablespoons of dough onto the prepared baking sheets, spacing them about 1½ inches apart.
Bake until the cookies are puffed and crackled, about 8–10 minutes.
Immediately after removing the cookies from the oven, use the rounded side of a ½‑teaspoon measuring spoon to make a deep well in the center of each cookie.
Let the cookies rest on the baking sheet for 4–5 minutes, then transfer them to a wire rack to finish cooling completely.