Preheat the oven to 350°F (177°C). Grease a 9x13 inch pan and set aside.
Using a fork or a mixer mash/puree the bananas until almost lump free.
In a medium bowl whisk together: flour, baking powder, baking soda, cinnamon, nutmeg and salt. Set aside.
Using a mixer fitted with the paddle attachment, beat the butter on high speed until smooth and creamy, for about 1 minute.
Add white and brown sugar and beat on high speed for 2 minutes. Using a spatula, scrape down the sides and up the bottom of the bowl as needed.
Add the eggs and vanilla extract. Beat on medium-high speed until combined.
Add the mashed bananas and with the mixer on medium speed, beat to combine. With a spatula, scrape down the sides and up the bottom of the bowl as needed.
With the mixer on low speed, add the dry ingredients in three additions alternating with the buttermilk and mixing after each addition just until incorporated, careful not to overmix.
With a spatula or with the mixer on low speed, stir in the very finely chopped walnuts. You can also grind them in a food processor if you prefer a finer texture.
Spread batter into the prepared pan.
Bake for 45-50 minutes. Start checking on the cake after 40 minutes, as baking time may vary. A toothpick inserted in the center comes out clean and the cake will look golden with slightly brown edges. If the top of the cake is browning too quickly in the oven, loosely cover it with aluminum foil.
Remove the cake from the oven and set on a wire rack to cool completely.