Preheat oven to 350 degrees.
In medium bowl, whisk together all-purpose flour, baking soda and salt.
Whisk in sugar.
In small bowl, combine eggs and vanilla. Add to dry mixture.
Add mashed overripe bananas and melted butter. Stir until well combined. Set aside.
Generously grease a standard bundt pan with vegetable oil. Be sure to grease center tube. Pour in batter. Tap pan on counter to evenly settle batter.
Use a damp cloth or paper towel to wipe off excess batter on edges and center tube.
Place bundt pan in oven. Reduce temperature to 325. Bake 30-35 minutes or until knife inserted in center comes out clean. Oven temperatures vary. Adjust cooking time and temperature when necessary.
Delicious warm or cold.
Although good fresh from oven, banana bread is much better after 24 hours in fridge. If desired, place whole cake or slices in a container, secure lid. Refrigerate 24 hours before serving.