Preheat the oven to 325 degrees F. Line the bottom and all 4 sides of an 8 inch square pan with foil. Position a rack in the lower third of the oven.
Melt the butter in a medium, heatproof bowl set directly in a wide skillet of barely simmering water. Add the sugar, cocoa and salt. Stir until the ingredients are blended and the mixture is hot. Remove the bowl from the skillet and set aside briefly until the mixture is only warm, not hot.
Mix in the vanilla, then add the eggs, one at a time, mixing vigorously with a rubber spatula after each addition. When the mixture looks thick, shiny, and well-blended, add all of the flour at once and stir until you cannot see it any longer. Then mix vigorously for 40 strokes with a wooden spoon or rubber spatula. Spread the batter evenly in the lined pan.
Bake for 20 to 25 minutes, until a toothpick plunged into the center emerges slightly dirty looking. Cool on a rack. Lift the edges of the foil liner and transfer the brownies to a cutting board. Cut into 16 or 25 squares. May be kept in a covered container for 2 to 3 days.
Notes
Gluten free folks: I have not tried this recipe as gluten free yet, but there is not a whole lot of flour in the recipe, just ⅓ cup, so I'm hoping that a gluten free flour blend can be substituted in this recipe without too much trouble. If you try it, please let me know of your experience with it!