1. Heat the oven to 350 degrees F. Lightly flour a 9 x 9 inch square cake pan (do not use a smaller pan) and dust it with flour, knocking out the excess.
2. Cut the butter into 1/2 inch pieces and place them in the top of a double boiler over barely simmering water. As the butter melts, sprinkle the chocolate evenly into it. Leave the mixture over the heat for 5 minutes, then stir or whisk until smooth. Transfer the top of the double boiler to a cooling rack and let the chocolate cool to room temperature.
3. 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 30 seconds, with an electric mixer set on medium-high. Blend in the vanilla extract. Add the cooled chocolate (which should still be liquid) and mix at medium speed just until evenly blended.
4. 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, if desired. Scrape the batter into the prepared pan and smooth it with a spoon.
5. 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 over-bake. For the best results, use 3 toothpicks to test for doneness. Insert on into the brownies about 1 inch from the side; it should come out clean. A second toothpick inserted 2 inches from the side should have a little batter stuck to it, and a third, inserted in the center, should be coated with a bit more batter then that.
6. 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 cool or at room temperature.
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