Preheat oven to 350°F. Line two baking sheets with parchment paper and set aside.
Melt the chocolate and butter in a double boiler or thick-bottomed sauce pan. Set aside to cool slightly.
In the bowl of a stand mixer, combine granulated sugar, brown sugar, egg and vanilla. Mix on medium speed until light and fluffy, 4-5 minutes. With the mixer on low, slowly add the chocolate mixture.
In a small bowl, whisk together the flour, espresso powder, cocoa powder, baking powder and salt. Add the flour mixture to the chocolate mixture, using a spatula to fold until combined. The dough will seem wet for a cookie dough.
Use a cookie scoop to scoop 2 Tablespoonfuls onto the prepared baking sheet. Make sure there is room between each cookie as they will spread. If using a half-sheet pan, I suggest making 6-8 cookies per sheet. Sprinkle with flaky sea salt.
Bake for 12-13 minutes. Remove from the oven and use a sturdy glass to swirl the cookies while still warm to make them perfectly round. Let the cookies cool on the sheet for 10 minutes, then transfer to a cooling rack to cool fully.