Preheat your oven to 350°F (175°C). Lightly grease a 9x5 inch loaf pan.
In a large bowl, whisk together the flour, baking soda, and salt.
In another bowl, cream together the butter and brown sugar until light and fluffy.
Beat in the eggs one at a time, then stir in the mashed bananas.
Fold the banana mixture into the dry ingredients just until moistened.
Pour the batter into the prepared loaf pan.
Bake for 60–65 minutes, or until a toothpick inserted into the center comes out clean.
Let the bread cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.