In a medium microwave-safe bowl, add the semi-sweet baking morsels and butter. Heat in the microwave for 15 seconds. Stir and then heat for another 15 seconds. Stir. If the chocolate is mostly melted do not heat again. (If the chocolate seizes or hardens a bit it is ok.) Set aside.
While the chocolate is cooling, add sugar, eggs, milk, and vanilla to a large bowl. Whisk well until they are completely incorporated, light, and airy.
Add the slightly warm chocolate to the egg mixture and whisk continuously until fully combined and smooth.
Add the flour, cocoa powder, baking powder, salt, and espresso powder. Stir well to incorporate, but don't over mix. The mixture should be very loose, just like a brownie mix.
Using a 2 tablespoon scoop, scoop out balls and place on the prepared baking sheet. Six cookies should easily fit on a 10x15 sheet, as they do not spread too much.
Press 5-9 chocolate morsels on top of each cookie and press down slightly, so the cookies are not rounded or domed.