Cut the butter into 1/2-inch pieces and place them in the top of a double boiler in which the water is barely simmering or in a heatproof bowl in the top of a saucepan of boiling water.
As the butter melts, sprinkle the chocolate evenly into it. Leave the mixture over the heat for 5 minutes, then stir or whisk it until smooth. Transfer the top of the double boiler or the bowl to a cooling rack and let the chocolate cool to room temperature.
Meanwhile, heat the oven to 350º. Lightly butter a 9- by 9-inch square cake pan and dust it with flour, knocking out the excess.
Combine the sugars in a large mixing bowl, using your fingers to break up any lumps. Add the eggs. Beat the eggs and sugar until well blended - about 2-3 minutes by hand or 30 seconds with an electric mixer set on medium-high speed. Blend in the vanilla extract. Add the cooled chocolate (which should still be liquid) and mix by hand or on medium speed until evenly blended.
Sift the flour and salt into a medium bowl, then stir them into the chocolate mixture, about half at a time, until no streaks of flour remain. Stir in the nuts. Then scrape the batter into the prepared pan and smooth it with a spoon.
Bake the brownies on the center oven rack for 30 to 35 minutes. When done, the brownies will have risen slightly and the top will have a thin, brittle crust. DO NOT OVERBAKE. For the best results, use 3 or 4 toothpicks to test for doneness. Insert one into the brownies about 1 inch from the side; (it should come out clean). A second toothpick inserted 2 inches from the side (it should have a little batter stuck to it), and insert the third and fourth if decided near the center, (they should be coated with a bit more batter than stick 2).
Transfer the pan to a wire rack and cool the brownies thoroughly. To get the cleanest cuts, cover and refrigerate the brownies for several hours before slicing. Serve slightly cool or at room temperature.
For Best results I find it better to mix all the ingredients by hand but if you‘re lazy or short of time you can always use a mixer....
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