Set the oven to 350 degrees Fahrenheit (175 degrees C). Grease a 9x5-inch loaf pan very lightly.
In a big bowl, mix the flour, salt, and baking soda. In a different big bowl, combine butter and brown sugar and blend with an electric mixer until smooth. Add eggs and mashed bananas; mix thoroughly. Just combine the flour mixture with the banana mixture. Fill the prepared loaf pan with the batter.
Bake in the preheated oven for about 60 minutes, or until a toothpick inserted in the centre comes out clean. Bread should cool in the pan for ten minutes before being removed to finish cooling on a wire rack.