Preheat the oven to 350°F and line 2 cookie sheets with parchment paper.
In a stand mixer with a whisk attachment, combine the eggs and both sugars. Beat on high speed for 7 minutes (set a timer) until the sugar dissolves. The mixture will be thick and fluffy and pale light brown in color.
In a microwave-safe bowl, combine the butter and finely chopped chocolate. Microwave in 30-second increments, stirring well between each increment, until the chocolate is completely smooth and melted. Do not overheat the chocolate as this can burn it. Set aside.
Once the eggs and sugars have been fully mixed for 7 minutes, add the vanilla extract to the bowl, then slowly pour in the melted butter-chocolate mixture. Mix on high speed until combined, about 30-45 seconds. Scrape down the sides.
Add the gluten-free flour, cocoa powder, salt, and baking powder. Mix until just combined, then turn off the mixture. Using a spatula, scrape the bottom of the bowl to fold in any remaining flour bits. The dough will be glossy and soft, similar to brownie batter
To get the distinct glossy crackly tops, do not let the dough sit! As soon as the dough is mixed, use a large #20 cookie scoop (around 3 tablespoons) to scoop the cookies onto the prepared sheets, placing them about two inches apart.
Bake one tray at a time for 8-10 minutes, or until the edges are set, but the center is still gooey. Remove the cookies from the oven and sprinkle with flaky sea salt. The cookies should have a beautiful crinkle top and be slightly domed. To achieve perfect round cookies, place a large cookie-cutter or glass cup slightly bigger than the cookies over the top of the cookies, and carefully swirl in a circular motion until they form a perfect circle. Cool for 5 minutes on the baking sheets before transferring them to a wire cooling rack to finish cooling.