Preheat oven to 375°F. Line 2 baking sheets with parchment paper.

In a small bowl, whisk together the flour, baking powder, and salt. Set aside.

In the bowl of an electric mixer with the whisk attachment, briefly whip the eggs to break them up. Add the sugar, espresso, and vanilla and whip on high speed for 15 minutes, until thick. (This will help add body to the batter because there is so little flour in the recipe.)

While the eggs are whipping, place the butter in the top of a double boiler, or in a small metal bowl suspended over a pot of simmering (not boiling) water, and scatter the extra-bittersweet and unsweetened chocolate on top. Heat until the butter and chocolate melt. Remove the boiler top from over the water and stir the chocolate and butter until smooth.

When the egg whites are done, remove the bowl from the mixer. Gently fold the chocolate mixture into the egg mixture until partially combined (there should still be some streaks). Add the flour mixture to the batter and carefully fold it in. Fold in the chocolate chips. If the batter is very runny, let it rest until it thickens slightly, about 5 minutes.

Drop the batter by heaping teaspoonfuls onto the prepared baking sheets and bake until puffed and cracked, 8 to 9 minutes. Cool on a wire rack before removing from the baking sheets.