In large bowl, sift together flour, baking powder, and salt. In standing mixer fitted with paddle attachment, beat butter until fluffy, about 3 minutes.
Add sugar and beat until light and fluffy, about 2 minutes more.
Add eggs 1 at a time, beating after each addition, then beat in vanilla.
Add flour mixture and beat on low just until combined.
Divide dough in half. Form 1 half into 4- by 4-inch square, wrap in plastic wrap, and set aside. Return other half to mixer. In metal bowl set over pan of barely simmering water, melt chocolate, stirring until smooth.
Add melted chocolate to dough in mixer and beat just until combined. Form chocolate dough into 4- by 4-inch square and wrap in plastic wrap. Refrigerate both squares of dough 30 minutes.
Line large baking sheet with parchment paper.
Cut each dough square into 4 strips.
Place 3 strips of chocolate dough and 4 strips of vanilla dough on baking sheet and refrigerate. Between 2 sheets of parchment paper, roll out 4th strip of chocolate dough into 6- by 7-inch rectangle (use ruler to make sure dimensions are exact).
Remove 1 strip of vanilla dough from refrigerator and, between 2 sheets of parchment paper, roll out into 6- by 6-inch square. Peel off top sheet of parchment from each dough and flip vanilla dough over onto chocolate, aligning top and bottom edges and allowing 1/2 inch of chocolate dough to stick out on each side. Run rolling pin lightly over doughs to adhere, then peel off top sheet of parchment. Fold extra 1/2 inch of chocolate dough over vanilla on 1 side. Starting on folded-over side and using parchment as aid, tightly roll up dough into log. Wrap in plastic wrap and refrigerate. Repeat with remaining strips of dough to form 4 logs.
Keep dough frozen until ready to slice and bake. Preheat oven to 350°F and grease 2 large baking sheets. Using sharp knife, slice dough into 1/4-inch-thick slices and place 1 1/2 inches apart on baking sheet.
Bake until vanilla dough is slightly golden, 9 to 11 minutes. Makes 20 cookies.
