Preheat oven to 375 degrees F (190 degrees C). In a large bowl, cream together the butter and sugar. Stir in the egg and vanilla.
In a separate bowl, combine the flour, baking soda and salt, stir into the creamed mixture. Finally, stir in the white chocolate and nuts. Chill for about 1 hour in the refrigerator. 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.