Preheat oven to 375 degrees Fahrenheit. Line 2 baking sheets with parchment paper and set aside.
Whisk together the all-purpose flour, whole-wheat flour, salt, and baking soda in a small bowl and set aside.
Whisk the butter, granulated sugar, and brown sugar on medium speed until pale and fluffy. Reduce speed to low and add egg and vanilla.
Mix the banana into the butter mixture. Add the flour mixture to the butter mixture. Stir in the oats, chocolate chunks, and walnuts, until just combined
Scoop the cookie dough using a 1 ½-inch ice cream scoop, and drop the dough 2 inches apart on your parchment-lined baking sheets.
Bake cookies until golden brown 12 to 13 minutes. Let them cool on a wire rack. Cookies can be stored in airtight containers for up to 2 days.