PREHEAT oven to 325°F. Microwave semi-sweet and unsweetened chocolates and butter in large microwavable bowl on HIGH 2 to 3 minutes or until butter is melted, stirring after 2 minutes. Stir until chocolate is completely melted. Cool to room temperature.
BEAT eggs and granulated sugar in large bowl with electric mixer on medium speed until well blended. Add chocolate mixture and vanilla; mix well. Blend in flour, baking powder and salt. Add white chocolate chunks and walnuts; mix well. Drop heaping tablespoonfuls of dough, 2 inches apart, on greased baking sheets.
BAKE 10 minutes or until cookies are slightly cracked but still moist. Cool 2 minutes; remove from baking sheets. Cool completely on wire racks. Sprinkle evenly with powdered sugar.