In a medium bowl, sift the flour, cocoa, baking powder, and salt onto a piece of parchment or wax paper. Set aside. In a mixer, beat the butter and sugar until fluffy, about 2 to 3 minutes. Add eggs and vanilla, and mix until combined. On low speed gradually add the flour mixture and mix until incorporated. With a wooden spoon, mix in the walnuts. Add the melted chocolate and milk, and stir to combine well. Refrigerate dough until firm, about 30 minutes.
Preheat the oven to 350 degrees F.
Roll dough into 1 1/2-inch logs and refrigerate until firm, about 30 minutes more. Cut logs into 1-inch slices and roll in confectioners' sugar. Transfer to an ungreased cookie sheet and bake until golden around the edges, about 10 to 12 minutes. Cool on wire racks.
A viewer or guest of the show, who may not be a professional cook, provided this recipe. It has not been tested for home use.