Preheat oven to 350 degrees F (180 C). Line a 9 inch square pan with foil.
Stir the sifted flour and salt together in a small bowl; set aside.
Melt the butter in a saucepan set over medium-low heat. When melted, reduce heat to low and add chopped chocolate, stirring often until it melts. Add only 1 cup of the sugar to the mixture and stir for about half a minute. Remove pan from heat and pour into a mixing bowl. Stir in the vanilla.
Whisk the remaining 1 cup sugar and the eggs in a second bowl. Whisk only until combined – don’t over-beat. Gradually pour ONLY half of the sugar/egg mixture into the chocolate mixture, stirring gently so that eggs don’t set from the heat of the chocolate mixture.
Using a hand-held mixer, beat the REMAINING sugar/egg mixture on high speed until it becomes pale and thick (it should double in volume).
Carefully fold the whipped egg mixture into the chocolate mixture. Fold in the dry ingredients.
Scrape the batter into the 9 inch square pan and bake on center rack for 25 to 28 minutes. Mine are usually done in 28 minutes.
Let the brownies cool completely, then lift from the pan and cut.
I like to chill my brownies thoroughly before slicing.