Preheat oven to 350°F. Line an 8x8 inch baking dish with parchment paper.
Place butter in a microwave safe dish and heat till melted. Add chocolate chips and whisk till smooth. Transfer chocolate to a mixing bowl.
Add flour, salt, coffee, and sugar to the mixing bowl with the chocolate. Stir to just incorporate the flour. Add eggs, egg yolk, and oil. Mix until combined.
Transfer batter to baking dish and evenly. Bake for 40 minutes. When tested with a toothpick the toothpick should come out clean from the center.
Allow brownies to cool for at least 30 minutes before frosting. Spread frosting over brownies, cut, and serve.
For Mocha Frosting
Mix butter and confectioners' sugar together with a stand or electric mixer. Mix in coffee, chocolate, and vanilla extract and beat until smooth. Add milk by the tablespoon, blending well after each addition, until it reaches spreading consistency. If you need to use more milk please add slowly.