Beat butter, peanut butter, 1/3 cup granulated sugar and brown sugar in large bowl with mixer until light and fluffy. Add egg, milk and vanilla; mix well. Combine flour, nuts, baking soda and salt. Gradually add to butter mixture, beating after each addition until well blended.
Shape dough into 48 balls, each about 1 inch in diameter; roll in remaining granulated sugar. Place, 2 inches apart, on baking sheets.
Bake 9 to 10 min. or until lightly browned. Immediately press a chocolate piece into center of each cookie. (Cookie will crack slightly around edge.) Cool on baking sheets 1 min. Remove to wire racks; cool completely.