Several hours or the day before baking:
In a medium bowl, sift together the flour, baking powder, and salt. With an electric mixer, beat the butter and sugar until light and fluffy. Beat in the egg and vanilla, scrape down the sides of the bowl, and beat again until blended. Add the flour mixture, beating just until combined. Remove half the dough (about 9 oz.); set aside. Whisk the cocoa into the melted chocolate; add to the dough remaining in the mixing bowl and beat briefly to blend.
Divide the chocolate and vanilla doughs into 8-pieces each, more or less the same size. Recombine the pieces, alternately pressing the chocolate and vanilla pieces together, to create a marbled ball. On a lightly floured surface, roll and shape the ball into a 9-inch-long log. (Handle the dough as little as possible to keep the marbled pattern more distinct.) Wrap in plastic and chill until very firm, 2 to 3 hours.
Heat the oven to 350°F. Cover your cookie sheets with parchment. Unwrap the firm dough and roll the log briefly on the counter to make it more evenly round. Cut it crosswise into 1/4-inch-thick slices; arrange the slices 1-1/2-inches apart on the sheets. Bake until the edges are lightly browned, 9 to 11 minutes, rotating the sheets from the top to bottom racks after 5 minutes. Let cool on the sheets for 5 minutes; transfer to a wire rack to cool completely.
Photo: Scott Phillips