Prepare the melted chocolate and butter. In a heatproof bowl, combine the cut butter and chopped chocolate bars. Melt in the microwave or over low heat until smooth. Let cool for 5 minutes.
Preheat the oven to 350°F (177°C) and line a 9-inch square baking pan with parchment paper.
Incorporate the sugars. Whisk the granulated sugar and brown sugar into the cooled chocolate mixture until glossy.
Add the eggs and vanilla; mix until fully incorporated and smooth.
Mix dry ingredients. In a separate bowl, whisk the flour, cocoa powder, and salt together.
Combine wet and dry. Gradually fold the dry mixture into the wet until no streaks remain.
Fold in chocolate chips, spread evenly in the pan, and bake for 32 to 35 minutes.
Cool completely in the pan on a wire rack.
Make the frosting by beating softened butter, then gradually adding confectioners’ sugar, cocoa powder, warm cream or milk, vanilla, and a pinch of salt.
Frost cooled brownies, lift from the pan, cut into squares, and serve.
Notes
For cleaner cuts, chill the frosted brownies briefly before slicing.