Preheat oven to 350°. Melt butter in a small saucepan over low heat. Remove from heat, and add brown sugar; stir until smooth. Combine all-purpose flour, whole-wheat flour, baking soda, oats, and salt in a medium bowl. Combine butter mixture with the dry ingredients, and add egg and vanilla extract. Fold in walnuts and bittersweet chocolate. Mix well, and spoon by tablespoonfuls onto lightly greased baking sheets. Bake for 12 minutes or until tops are dry to the touch.