Melt white chocolate in a small saucepan over low heat, stirring until chocolate is smooth.
Beat butter and 1 cup sugar at medium speed with an electric mixer 5 minutes or until fluffy. Add eggs, 1 at a time, beating until blended. Add vanilla, beating well. Add melted chocolate, and beat 30 seconds.
Combine flour and next 3 ingredients; add to butter mixture, beating until blended. Stir in walnuts. Drop dough by heaping tablespoonfuls onto lightly greased baking sheets.
Bake at 350° for 10 to 12 minutes or until edges are lightly browned. Remove to wire racks to cool completely. Sprinkle with powdered sugar. Freeze, if desired.