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.