HEAT oven to 350°F.
BEAT butter and sugars in large bowl with mixer until blended. Add eggs, 1 at a time, mixing on low speed after each just until blended. Combine flour and baking soda; gradually beat into butter mixture.
DIVIDE dough in half; place in separate bowls. Add melted chocolate to dough in one bowl; mix well. Stir in white chocolate pieces and nuts.
STIR chocolate chips into dough in second bowl. For each cookie, drop 1 tsp. of each dough, side by side, onto baking sheets, leaving 2 inches between cookies.
BAKE 8 to 10 min. or until lightly browned. Cool on baking sheet 3 min. Remove to wire racks; cool completely.