Start by preheating your oven to 350°F (175°C). Line your baking trays with parchment paper so the cookies release cleanly and bake evenly.
In a bowl, whisk together the all-purpose flour, whole wheat flour, baking soda, and salt. Mixing the dry ingredients first makes sure everything distributes evenly before combining with the wet mixture.
In another bowl, cream the butter with the white and brown sugar until light and fluffy. Add the egg and vanilla, mixing just until combined. Gently stir in the mashed banana until the mixture looks smooth and blended.
Fold the dry mixture gradually into the wet mixture until just combined. Add the rolled oats, chocolate chips, and walnuts if using, and mix until everything is evenly distributed without overmixing.
Scoop the dough onto your baking sheet, spacing each portion about 1½ inches apart. Bake for 6 minutes, rotate the tray, then continue baking another 6–7 minutes until golden around the edges.
Let the cookies cool on the baking sheet for 5 minutes to firm up. Transfer them to a wire rack to cool completely — though they’re amazingly warm!