Position rack in center of oven and preheat to 350 degrees. Line 3 cookie sheets with parchment or nonstick baking liners.
In a medium bowl, whisk the flour, salt, baking powder, and baking soda.
In a stand mixer fitted with the paddle attachment, beat butter, sugar, and cocoa powder on medium speed until well blended, about 2 minutes. Scrape down the bowl and the beater. Add the eggs one at a time, mixing until blended after each addition, about 30 seconds, and adding the vanilla along with the last egg, Continue mixing on medium speed until well blended, about 1 minute. Add the cooled melted chocolate and mix until just blended, about 30 seconds. Add the flour mixture and mix on low speed until well blended, about 1 minute.
Using a mini ice cream scoop, drop tablespoons of dough about 1 1/2" apart on the prepared cookie sheets. Bake, one sheet at a time, until the cookies are puffed and the tops cracked and dry, 11 to 13 minutes. When the cookies are just out of the oven, use the rounded side of a 1/2 teaspoon measure or the end of a thick wooden spoon to make a small deep well in the center of each cookie. Let the cookies sit on the cookie sheet for 5 minutes and then transfer them to a rack to cool completely. At this point, you can fill the cookies immediately, or store in an airtight container at room temperature for up to 3 days, or freeze for up to one month before filling.
Filling: Melt chocolate and butter in the microwave or in a medium bowl set in a skillet of barely simmering water, stirring with a rubber spatula until smooth. Remove from the heat and set aside until cool and slightly thickened.
Sppon the chocolate mixture in the the wells of the cooled cookies. Set aside until the chocolate firms up, about an hour. Serve immediately or store in an airtight container at room temperature for up to 3 days,.