Line the 8"x8" baking pan with aluminum foil. The easiest way to form the foil is to mold and fold the whole piece over the outer side of the pan, then place it inside.
Preheat the oven to 400°F and place the baking rack 1/3 of the way from the bottom.
Completely melt butter and chocolate in a medium heatproof bowl propped over a saucepan of simmering water (about an inch high of water). Make sure the bowl doesn't touch the water. Stir occasionally for faster melting.
As soon as the butter and chocolate are melted, set bowl on the counter. Mix in sugar, vanilla extract, and salt using a spatula.
Stir in the eggs one at a time until incorporated.
Fold the flour into the mixture and then stir vigorously to achieve a consistently smooth and glistening batter. It will start to pull away from the sides of the bowl.
Pour the batter into the baking pan lined with aluminum foil. Level the top and bake for 20 minutes.
Fifteen (15) minutes into baking (or 5 minutes before the baking time is over), prepare the ice bath: add ice cubes in the bigger pan and fill with water halfway from the bottom.
Remove the pan from the oven and immediately (but carefully) place into the ice water bath. Avoid splashing water into the brownies.
Let it cool completely in the ice bath. Ease the aluminum foil with brownie out of the pan, peel the foil off and place on a cutting board for cutting and serving.