Preheat the oven to 350°F (175°C) and grease a 9x5-inch loaf pan.
In a bowl, whisk together flour, baking soda, and salt. Set aside.
In another bowl, cream butter and brown sugar until smooth, then mix in beaten eggs.
Mash overripe bananas and stir them into the wet mixture.
Gradually add the dry ingredients to the wet mixture, stirring until just combined.
Pour the batter into the loaf pan and smooth the top.
Bake for 55-60 minutes or until a toothpick inserted in the center comes out clean.
Let it cool in the pan for 10 minutes, then transfer to a wire rack. Slice and enjoy!