Sift together the flour, cocoa, baking powder, and salt. Set aside.

Cream butter and sugars until light and fluffy. Beat in eggs, one at a time, beating after each addition. Beat in vanilla.

On low speed, beat in flour mixture a little at a time, until well blended and smooth. Stir in chopped walnuts.

Drop chocolate cookie dough onto greased baking sheets by rounded tablespoons, about 2 inches apart. Bake at 350° for 12 to 15 minutes, or until set. If desired, sprinkle with a little granulated sugar while they're hot.

Cool on pans on rack for about 5 minutes; transfer chocolate cookies to rack to cool completely.