Have all ingredients at room temperature (68-70 degrees). Postition a rack in the center of the oven, preheat to 350 degrees. Line a 13x9 inch baking pan with greased aluminum foil, allowing it to overhang the 2 narrow ends of the pan by about 2 inches.
In a large, heavy saucepan over very low heat, melt the chocolate and butter, stirring constantly until the mixture is smooth. Set aside to cool completely. Stir in the sugar and vanilla. Stir in the 4 large eggs, until well combined. Stir in the flour and nuts, until *just* combined.
Scrape the batter into the pan and spread to the edges. Bake until the center is almost firm when lightly pressed and a toothpick inserted in the center comes out clean, but still moist at the bottom, 23 to 28 minutes. Remove the pan to a rack and let stand until completely cool. Using the overhanging foil as handles, lift the brownie to a cutting board. Carefully peel off the foil. Cut into bars.