Preheat oven to 400 degrees F. Line a 9 inch square metal baking pan with nonstick foil or parchment paper.
Melt butter in a saucepan. Reduce heat to low and add chocolate. Stir until melted; set aside. Alternately, you may melt them together in a double boiler or using the microwave.
Beat eggs and salt in a stand mixer with the whisk attachment. With mixer going, gradually add sugar and continue to beat, increasing speed slightly, until mixture is pale and thick (about 10 minutes). Beat in the vanilla.
Remove mixer from the stand and with a heavy duty scraper, stir in the melted chocolate. When chocolate is incorporated, stir in the flour.
Scrape the batter into the pan and put in the oven.
Immediately reduce heat to 350 degrees F.
Bake for about 40 minutes or until tops appear set. A toothpick inserted in the center will not come out clean at this point, so the regular toothpick test won't work.
Let brownies cool completely. When cool, lift from pan and cut into large squares. For a cleaner cut, chill the brownies after they cool, then cut.