Preheat oven to 350 degrees F. Line a baking sheet with parchment paper.
In a medium bowl, whisk together flour, baking soda, cinnamon, nutmeg and salt.
In a large bowl, beat butter, oil and sugars until sugars have dissolved and mixture is light in color, about 1 minute.
Add egg, applesauce and vanilla and beat an additional 30 seconds.
Add flour mixture and beat an additional 30 seconds.
Add oats, flakes, raisins and walnuts (if desired) and mix over low speed just until incorporated.
Drop by tablespoons onto prepared baking sheet. Bake for 12 minutes, until cookies are fragrant but still soft. Let cookies cool slightly, then transfer to a wire rack to cool completely.