Preheat the oven to 350 degrees and grease two loaf pans with nonstick cooking spray.
Whisk together the flour, baking soda, cinnamon, nutmeg and salt until well combined. Set aside.
In a separate bowl, beat together the sugar, brown sugar, and butter until smooth.
Add the mashed bananas, vanilla and eggs and stir to mix.
Next add in the dry ingredients to the bowl and stir until just combined.
Fold in the chopped walnuts.
Pour the batter into the prepared pan and bake on middle oven rack for 50 to 60 minutes until the bread is golden brown on top and a toothpick inserted in the center comes out clean. Don't overbake.
Allow the bread to cool in the pan for five minutes, then transfer to a wire cooling rack to cool completely before slicing and serving.