Preheat the oven to 350 degrees F (180 degrees C) and grease a 9x5-inch pan (23x13 cm).
In a large bowl, mix the flour, baking soda, and salt. Set aside.
Mash the bananas in a small bowl using a fork and set aside.
In a separate bowl, beat the butter with the brown sugar for a few minutes using a hand mixer or spatula until light and creamy. Add the eggs one at a time, then add the mashed bananas and the vanilla extract and mix until combined.
Add the dry ingredients to the wet ingredients and mix until they are well combined, making sure not to overmix. Fold in the chopped pecans or walnuts, if using.
Pour the batter into the prepared loaf pan and bake for 60 minutes or until a toothpick inserted in the center comes out clean. Check the bread after 30 minutes, and cover with aluminum foil if you notice that the bread is turning dark on top. Let the banana bread rest for 10 minutes before slicing and serving.