Heat oven to 350°F. Line cookie sheets with parchment paper. (Cookie sheets need to be heavy to prevent bottoms of cookies from scorching. Use one sheet on top of another, if necessary.)
Onto sheet of waxed paper, sift together flour, cocoa, baking powder, cream of tartar and salt.
Place melted butter in large bowl. Over butter, sift Vanilla-Scented Confectioners Sugar; mix in with wooden spoon. The mixture will have small lumps of confectioners sugar. Blend in vanilla extract and walnuts. Stir in half of sifted flour mixture and all the chocolate chips. Stir in half of the remaining flour mixture, then the rest. Dough will be malleable.
For each cookie, roll scant 1 tablespoon of dough into a ball. Place balls about 2 inches apart on lined cookie sheets, 12 to 16 balls per sheet.
Bake in 350°F oven for 13 to 15 minutes or until set; tops will crack slightly here and there. Let cookies stand on sheets 1 minute. Using offset metal spatula, carefully remove cookies to cooling racks. Let cool 5 to 8 minutes.
Sift together confectioners sugar and cocoa into large bowl. While cookies are still warm, dredge them, a few at a time, in sugar-cocoa mixture to coat; transfer to waxed paper to cool. Dredge them lightly again, if you wish. Store airtight at room temperature up to 5 days.
Split open sides of vanilla beans. Pour 1 pound of the confectioners' sugar in large storage container; drop in one split bean. Fill with half the remaining sugar; drop in remaining bean. Add rest of sugar. Cover tightly. Stir after 2 days. Let sit another 2 days before using.