Heat the oven to 350F. Grease a 9x9 metal baking pan and line it with parchment paper, leaving ends overhanging.
Fill a medium pot with a couple inches of water and bring it to a near simmer (steaming but not bubbling) over low heat. Add the butter and chocolate to a heat proof glass bowl which fits over the top of the pot.
Place the bowl over the steaming water and melt the chocolate and butter. Stir occasionally with a silicone spatula until smooth.
Take the bowl off the heat and place it on a kitchen towel. Add the cocoa powder and espresso powder. Whisk until smooth.
Combine the sugar, eggs, vanilla, and salt in a large bowl. Whip with a hand mixer until the mixture is thick and light colored, about 5 minutes.
Pour the chocolate into the egg mixture and combine.
Sift the flour over and lightly mix the flour into the batter. Mix with a large spatula only until there are no streaks flour left.
Pour the batter into the prepared baking pan and smooth out the top. Bake for 20-25 minutes, or until the temperature of the brownies reaches 200-205F.
Set the pan over a cooling rack. Cool the brownies in the pan for 15 minutes. Pull them out using the parchment overhangs and let them cool to room temperature on the cooling rack.