In a medium bowl, cream together the butter and sugar. Stir in the egg and vanilla. Combine the flour, baking soda and salt, stir into the creamed mixture. Finally, stir in the white chocolate and nuts. Drop cookies by heaping teaspoonfuls onto an ungreased cookie sheet, about 2 inches apart.
Bake for 8 to 10 minutes in the preheated oven, until lightly browned. Cool on wire racks. When cool, store in an airtight container.