Preheat oven to 350F. Line a large baking sheet with parchment paper; set aside.

In a medium saucepan, melt the butter over medium heat and cook until bubbling (but do not allow the butter to brown).

Add the chocolate chips, cocoa powder, and espresso powder in a medium mixing bowl. Pour the hot butter over the mixture and set aside to melt for a few minutes, then stir until smooth.

In a large mixing bowl or the bowl of a stand mixer, beat the eggs, granulated sugar, and brown sugar together with an electric mixer or stand mixer on medium-high speed until very light and fluffy, about 5 minutes.

Pour the melted chocolate mixture and vanilla extract into the beaten eggs and mix on low speed until combined.

Add the flour and mix on low speed just until incorporated, but do not over-mix.

Scoop the dough onto the prepared baking sheet in 2 tablespoon (1 ounce) dough balls. Leave 2-inches between each dough ball. For cookies with a smooth top surface, roll the balls between your lightly oiled palms to create smooth dough balls.

Bake the cookies at 350F for 8-10 minutes until set. Cool on the baking sheet for 5 minutes then transfer to a wire cooling rack to cool completely to room temperature.