Center a rack in the oven and preheat the oven to 325 F. Line an 8-inch square baking pan with foil; butter the foil and set aside. Set a heatproof bowl over a saucepan of simmering water (making sure the bowl doesn't touch the water). Put the 5 tablespoons of butter in the bowl, add the chocolate pieces, and stir occasionally until the ingredients are just melted—you don’t want them to get so hot that the butter separates. Remove the bowl from the pan of water; stir well to combine and ensure that all the chocolate is melted.
With a spatula, stir the sugar into the chocolate mixture and combine. (Don’t be concerned when your smooth mixture turns grainy.) One by one, add the eggs and stir well to combine. Add the vanilla and give the ingredients a vigorous mix before gently stirring in the espresso, if you’re using it, then the salt and flour. Stir only until incorporated. Fold in the chopped walnuts.
Scrape the batter into the pan and smooth the top with the spatula. Bake for 30—33 minutes, or until the top is matte and a thin knife inserted into the center comes out clean. Transfer the pan to a cooling rack and cool the brownies to room temperature.
When the brownies are completely cool, remove them from the pan using the foil. Peel away the foil and invert brownies onto a cutting board. Cut into 16 squares, each a scant 2 inches on a side.