Preheat the oven to 350°F. Line a 9x5-inch loaf pan with parchment paper and lightly grease the short sides of the pan where parchment isn’t touching.
In a large bowl, combine the mashed bananas with the sugar, oil, milk, eggs, and vanilla and whisk until combined.
In a medium bowl, combine the flours, baking powder, baking soda, salt, cinnamon, and nutmeg.
Add the dry ingredients to the bowl with the wet ingredients and stir until just combined, then fold in the walnuts.
Pour into the prepared pan and sprinkle with the chopped walnuts and oats.
Bake for 42 to 48 minutes, or until a toothpick inserted in the middle comes out mostly clean.