Preheat the oven to 375°F and line 2 baking sheets with parchment paper. Set aside.
In a small bowl whisk together both flours, salt, and baking soda.
Combine the butter and both sugars in the bowl of an electric mixer fitted with the paddle attachment; mix on medium speed until pale and fluffy. Reduce the speed to low and add the egg and vanilla; mix well to incorporate. Mix in the banana. Add the flour mixture all at one time and mix until just combined. Gently fold in the oats, chocolate chips, and walnuts.
Using a 1 1/2-inch cookie scoop , drop the dough into the prepared baking sheets about 2 inches apart. Bake, rotating the pans halfway through, until golden brown and just set. Approximately 12-13 minutes. When done baking allow the cookies to cool for at least 5 minutes on the sheet pans on wire racks before transferring the cookies to the racks to cool completely. Cookies can be stored in an airtight container for up to 2 days.