Peel the bananas and put them in a mixing bowl. Beat them with an electric mixer until fairly smooth (a couple of minutes). If the bananas are not ripe there will be lumps.
add 1 egg, 1 cup sugar, and 1/2 teaspoon salt. Mix well, then add 1 1/2 cups flour, 1 teaspoon baking soda. Mix again and slowly add 1/4 cup melted butter.
Pour into greased loaf pan, sprinkle sugar on top, and bake in a preheated 350 degree oven for about 45 mins to an hour, or until center springs back when pushed (or when knife inserted in center comes out clean, or however you like to check for doneness). It will be quite dark.
Cool 10 minutes, then loosen sides with knife and remove from pan to wire rack(s) to cool. It's wonderful warm with real butter on it!
***NOTES*** It takes three bananas to make one loaf, so you can freeze your rotten bananas until you have enough for a loaf or two. It's a great use for your bananas that are too ripe to eat; Now you don't have to throw them away. There's no need to bag them. Just throw them in the freezer in their skins and they'll keep for quite awhile. When you're ready to make your bread, thaw them on something that won't stain, like a glass or ceramic plate, not on a formica counter or a melamine plate. They will ooze liquid when they thaw.