Line the bottom and sides of an 8-inch square pan with parchment paper or foil. Position rack in the lower third of the oven and preheat to 325 degrees.
Set a medium heatproof bowl in a skillet. Add 1 inch of water. Bring water to barely simmering over medium-low heat. Add butter, sugar, cocoa powder, and salt. Stir until butter is melted and the mixture is hot. Remove the bowl from the skillet and allow to cool briefly until the mixture is warm, but not hot.
Stir in vanilla. Add the eggs, one at a time, mixing vigorously with a spatula after each one. When the mixture looks thick, shiny, and well blended, add all the flour at once and stir until you cannot see flour any longer. Then mix vigorously 40 strokes with a wooden spoon or rubber spatula. Sir in the nuts if using.
Spread batter evenly in the lined pan. Bake 20 to 25 minutes until a toothpick plunged into the center emerges with a very thin film of batter. Cool on a wire rack. Lift the edges the parchment or foil liner and transfer brownies to a cutting board. Cut into 16 or 25 squares. Brownies can be stored, airtight, for 2-3 days.