Preheat oven to 325°F. Line two cookie sheets with parchment paper.
In a microwave-safe bowl, combine the semi-sweet chocolate morsels and butter. Heat in the microwave for 15 second increments, stirring after each one, until the mixture is smooth. If the chocolate seizes or hardens a bit, that is okay. Set the chocolate aside to cool.
In a large bowl, whisk together the sugar, eggs, milk, and vanilla extract until they are completely incorporated and the mixture is light and airy.
Slowly add the slightly warm chocolate to the egg mixture, whisking continuously until it is fully combined and smooth.
Add the flour, cocoa powder, baking powder, salt, and espresso powder to the bowl and stir well to incorporate, being careful not to overmix. The mixture should be very loose, similar to a brownie mix.
Place the bowl of dough in the freezer for 15 minutes.
Using a 2-tablespoon scoop, portion out the cookie dough onto the prepared baking sheets. You should be able to fit 6 cookies on each sheet, as they do not spread too much.
Press 5-9 chocolate morsels onto the top of each cookie, pressing down slightly to flatten them.
Bake the cookies for 11-14 minutes, or until the center portion no longer appears wet.
Allow the cookies to cool on the pan for at least 3 minutes before transferring them to a wire rack to cool completely.