Adjust two oven racks to the upper- and lower-middle positions, and then preheat the oven to 350 degrees F.
Melt the unsweetened chocolate, bittersweet chips, and butter in heatproof bowl set over saucepan of simmering water, stirring frequently, until completely smooth and glossy. Remove the bowl from the pan and set aside to cool slightly.
Stir the coffee powder into the vanilla extract in a small bowl until dissolved.
Beat the eggs and sugar in large bowl with an electric mixer at medium-high speed until very thick and pale, about 4 minutes.
Add the vanilla-coffee mixture and beat until incorporated, 20 seconds. Reduce the speed to low, add the chocolate mixture, and mix until thoroughly combined, about 30 seconds.
Whisk in the flour, baking powder, and salt together in a medium bowl. Using large rubber spatula, fold the flour mixture and semisweet chips into the batter.
Cover the bowl with plastic wrap and let stand at room temperature until the batter firms up (it will more closely resemble thick brownie batter than cookie dough), 20 to 30 minutes.
Line two large baking sheets with parchment paper.
Using 1 heaping tablespoon batter per cookie, place the cookies 2 inches apart on the prepared baking sheets.
Bake until the cookies are shiny and cracked on top, 11 to 14 minutes, rotating the baking sheets from the top to bottom and the front to back halfway through baking time.
Transfer the baking sheets to racks and cool the cookies completely on the baking sheets, before serving.