Place your oven rack in the lower third of the oven. Preheat the oven to 325F. Line the bottom and sides of an 8-inch baking pan with parchment paper being sure to leave an overhang on the two opposite sides.
Combine the butter, sugar, cocoa, and salt in a large heatproof bowl and set the bowl in a wide skillet of barely simmering water. You want the bottom of the bowl to be able to sit in the water and not above it like with a double boiler. Stir occasionally until the butter is melted and the mixture is smooth. The mixture should be hot enough that you want to remove your finger fairly quickly after testing it.
Set aside the bowl until the mixture is only warm, not hot. The sugar may not be completely melted yet but it will continue to soften after the other ingredients are added.
Stir in the vanilla with a wooden spoon. Add the eggs the batter looks thick, shiny and well blended, add the flour and stir until you cannot see it any longer. Then beat vigorously for about 30 seconds with the spoon. At this point, stir in the nuts if using. Spread evenly in the lined pan.
Bake until a toothpick placed in the center comes out still slightly moist with batter, about 30 - 40 min. Don't overcook or you will lose the soft, fudge-like center. Let cool completely on a rack.
Lift up the ends of the parchment or foil liner, and transfer the brownies to a cutting board. Cut into 16 or 25 squares.