Preheat the oven to 325℉ (165℃). Line two baking sheets with parchment paper or silicon baking mats.
In a medium bowl, sift together the flour, cocoa powder, baking powder and salt. Whisk to combine and set aside.
Create a double boiler by filling a medium saucepan with 2 to 3 inches (5 to 7.5 cm) of water. Bring the water to a simmer over medium-low heat. Place a heatproof bowl over the pan, making sure the the bottom of the bowl does not touch the water below. Add the semi-sweet chocolate, bittersweet chocolate and butter and heat, stirring often. Do not overheat. Once melted, remove the bowl from the heat and stir until the mixture is smooth and shiny. Set aside to cool slightly.
In the bowl of a stand mixer fitted with the paddle attachment cream together the granulated sugar, brown sugar, eggs, espresso and vanilla until thickened, about 2 minutes. Add the chocolate mixture and blend on low speed until combined.
Add the flour mixture gradually and mix until barely combined. You should still see some streaks of flour in the batter. The batter will be soft, similar to cake batter. Remove the bowl from the mixer and gently fold in most of the chocolate chips, reserving 1 to 2 tablespoons for the tops of the cookies if desired. Do not overmix. Let the dough sit for 5 to 10 minutes at room temperature.
Use a 2 tablespoon cookie scoop to portion the cookie dough onto the prepared baking sheets, leaving 2 inches (5 cm) between each cookie. Bake in the center of the oven for 8 to 10 minutes, or until the edges are barely set and the centers of the cookies still look soft and fudgy. The cookies will continue to bake a bit once removed from the oven. As soon as the cookies are out of the oven, use the inside arch of a fork to nudge the edges of the cookie in toward the center, working your way around each cookie while they are still hot. This will help make the cookies more uniform in size and shape for the sandwiches.
Allow the cookies to rest for 6 to 8 minutes on the baking sheets before using a spatula to carefully transfer them to a wire cooling rack. Let cool completely before assembling the sandwiches.