Preheat oven to 350 degrees F and ready a 9 by 5-inch loaf pan, or 4 small loaf pans. In a large bowl, combine the flour, baking soda, and salt; set aside.

Mash 2 of the bananas with a fork in a small bowl so they still have a bit of texture. With a fork, whip the remaining bananas, sugar and brown sugar together until well mixed. Add the melted butter, eggs, and vanilla; beat well. Mix in the dry ingredients just until incorporated. Fold in the nuts and the mashed bananas. Pour the batter into the prepared loaf pan(s). Give the pan(s) a good rap on the counter to get any air bubbles out.

Bake for about 1 hour and 15 minutes (large pan) or 55 minutes (4 small pans), until golden brown and a toothpick inserted into the center of the loaf comes out clean.

Cool the bread in the pan for 10 minutes or so, and then turn out onto a wire rack to cool completely before slicing.