1) Into a bowl, sift together the sifted flour, baking powder, and salt.
2) Melt the butter and chocolate over hot water or very low heat.
3) In a mixing bowl, beat the eggs. Add the sugar to the eggs a little at a time, beating well. Blend in the chocolate and butter mixture. Stir in the flour mixture, blending well. Stir in the chopped walnuts and vanilla.
4) Spread the brownie batter in a greased and floured 8-inch square pan. Bake at 350° for about 25 minutes.
5) Cool in pan and cut into squares.