Move oven racks to upper and lower third of the oven. Preheat oven to 350 degrees. Line two 18 by 13-inch baking sheets with parchment paper.
In a medium mixing bowl whisk together flour, cocoa powder, baking powder and salt. Set aside.
Place chocolate and butter in a heat proof mixing bowl (such as a glass mixing bowl), set over a saucepan with 1-inch of barely simmering water set over low heat (aka a double boiler). Bowl should not be touching water.
Let mixture heat, stirring constantly with a silicone spatula and scraping along bowl, until chocolate and butter are just melted. Remove from heat and let cool until just warm, about 6 to 8 minutes.
Meanwhile add granulated sugar, brown sugar and eggs to a large mixing bowl. Using an electric hand mixer blend together on low speed until combined then increase to high speed and whip 4 minutes until pale, fluffy and slightly thickened.
Pour vanilla and slightly cooled chocolate mixture into egg mixture and blend with hand mixer on medium-low speed until combined.
Add in flour mixture then blend on low speed until just combined. Scrape bowl with a silicone spatula and gently fold from the bottom to ensure ingredients are evenly incorporated.
At this point the mixture should be almost like a typical brownie batter and fairly runny but if it's extra runny and won't hold any sort of rounded form when a spoonful is dropped then cover bowl and chill for 20 minutes (I don't have to do this step but there could be variances in chocolate brands and so forth so it is an option).
Drop mixture using a (slightly heaped) 1.5 Tbsp cookie scoop onto prepared cookie sheets spacing each about 3-inches apart. You should fit 12 per cookie sheet.
Bake in preheated oven on upper and lower racks for 5 minutes. Quickly rotate pans to opposite racks then continue to bake until cookies are puffed and crackled but they should appear slightly under-baked and still be soft to the touch, about 5 to 7 minutes longer.
Remove from oven and let cool on the baking sheets for 5 minutes. Then transfer to a wire rack to cool or enjoy cookies warm. If you'd like extra sweetness dust them with powdered sugar.
*With some brands this is considered bittersweet chocolate. Other brands it's semi-sweet chocolate. I use Ghirardelli 60% bittersweet chocolate bars here.