Preheat oven to 350°F and grease an 8×8 baking pan. Line with parchment to fit the bottom of the pan and overhang the sides. Grease parchment and set aside.
In a microwave-safe bowl, combine the chopped bittersweet chocolate and butter. Microwave in 30-second increments until the butter and chocolate are melted and combined. Set aside to cool slightly.
In a separate bowl, combine the flour, sugar, cocoa, espresso powder, and salt. Whisk to combine. Add eggs and vanilla to the melted chocolate, whisking to combine.
Add the eggs and chocolate mixture to the dry ingredients. Whisk or fold until only a few dry streaks remain. Do not over mix the batter or the brownies could become tough. Add chopped semi-sweet and milk chocolate. Fold to incorporate.
Pour batter into prepared pan and spread to an even layer. Place in preheated oven for 25-30 minutes. The edges will become set but the center will slightly jiggle. Do not overbake! If the center is completely set when you pull the brownies out, they will be dry and have less flavor!
Let cool completely in the pan for two hours. Remove brownies using parchment sling and slice.