Cream the butter and sugars together until light and fluffy. Beat in the egg and orange zest. Stir the flour, baking soda, and salt together; mix into the creamed mixture. Stir in the white chocolate chips and chopped walnuts. Drop tablespoonfuls of dough onto ungreased baking sheets.
Bake for 10 to 12 minutes in the preheated oven. Allow to cool on the baking sheet for 2 minutes before transferring to a wire rack to cool completely.