Line baking sheet with parchment paper.
Sift flour, cocoa, baking powder and salt into medium bowl. Using an electric mixer, cream sugar and butter in large bowl until smooth. Beat in eggs, one at a time, then vanilla. Turn mixer down to low and add in flour mixture, a little at a time. Stir in semisweet and white chocolate.
Drop dough by heaping tablespoonfuls onto prepared sheet in two 10-inch long strips, spaced three inches apart. Using metal spatula or wet fingertips, shape strips into 11-inch by 2 ½-inch logs. Refrigerate 30 minutes. Preheat oven to 350°. Bake logs until tops are cracked and dry and a toothpick inserted into center comes out clean, about 25 minutes. Let cool 10 minutes.
Reduce oven temperature to 300°. Lift logs onto work surface using parchment paper.
Place cooling racks on two baking sheets. Using a serrated knife, gently cut warm biscotti logs crosswise into ¾-inch slices. Arrange half of slices, cut side down, on each prepared baking sheet. Bake biscotti until just dry to touch, about 8 minutes. Turn biscotti over. Bake until top is dry to touch, about 8 minutes. Cool completely.
Variation: Dip finished biscotti in melted white chocolate.