Preheat the oven to 325 °F. Grease a 9x5 inch loaf pan and set aside.
Whisk together the flour, salt and baking soda in a bowl.
In a mixing bowl, beat together the butter and sugars until smooth. Beat in the eggs, one at a time until fully incorporated. Stir in the bananas and vanilla until mixed in,
Stir in the walnuts.
Slowly mix in the dry ingredients until incorporated, mixing on the lowest speed.
Bake for 60 to 70 minutes in the preheated oven, until a toothpick inserted into the middle of the loaf comes out clean.
Cool the loaf in the pan for 10 minutes, the remove from the pan and let cool completely on a wire baking rack.
Store at room temperature in a closed container or bag for 2-3 days.
Notes
There is no baking powder in this recipe on purpose : banana nut breads are supposed to be thick, dense and moist, not light and airy!