Preheat the oven to 350 degrees F. Grease an 8-inch square baking pan with butter; line the bottom with parchment paper, cut to fit, and then grease the parchment.
In the top of a double boiler over simmering water, heat the butter, chocolate and coffee, stirring occasionally, until the butter and chocolate have melted and the mixture is smooth. Remove from the heat and let cool slightly. With a wooden spoon or rubber spatula, beat in the sugar, vanilla and salt--the mixture will look grainy, but don't worry, it will come together later. Continuing with the spoon or spatula, beat in the eggs, one at a time, beating well after each addition. Add the flour and cocoa powder and beat for a full minute.
Scrape the batter into the prepared baking pan and smooth the top. Bake for about 30 minutes if using a metal pan (a little longer for glass or ceramic), until a toothpick inserted into the center comes out with a few moist crumbs clinging to it.
Set the pan on a wire rack until cool enough to handle, about 45 minutes. Run a thin knife around the sides of the pan, invert onto a large plate or cutting board, and peel off the parchment from the bottom of the released brownie. Flip back onto the rack to cool completely.
Transfer to a cutting board and cut into 2-inch squares, using a sharp knife.