Grease a 13x9x2-inch baking pan; set aside. In a heavy small saucepan, heat the butter and chocolate over low heat, stirring constantly, until chocolate is melted and smooth. Set aside to cool. In a small bowl, stir together flour, baking powder and salt. Set aside.
In a large mixing bowl, beat eggs and sugar with an electric mixer on high speed for 5 minutes or till lemon-colored and fluffy, scraping sides of bowl occasionally. Add cooled chocolate mixture and vanilla. Beat on low speed until combined. Add flour mixture. Beat on low speed till combined, scraping sides of bowl. Stir in walnuts. Spread the batter in the prepared pan. Bake in a 325 degree F oven for 30 minutes or until brownies appear set.