Preheat oven to 350 degrees F.
In the bowl of a stand mixer fitted with the paddle attachment, beat the eggs, white sugar, brown sugar and vanilla on high for at least ten minutes. You need a meringue type consistency in order to create a crust on top of the brownies.
In a separate bowl, add the flour, cocoa powder, espresso powder and salt. Stir to combine.
In a microwave safe bowl, add the butter and chocolate. Microwave on high for 30 seconds, stir and repeat until chocolate has completely melted and is smooth.
While the stand mixer is on medium speed, slowly add the chocolate until mostly combined. Add the flour mixture and stir until just combined.
Grease and flour a 9x13 inch baking dish. Pour batter into dish and smooth out the top. Bake for 25 minutes or until the top is matte and a bit cracked. Don't over bake. The brownies will set as they cool. Allow the brownies to cool for 10-15 minutes before you top them with the marshmallows.