In a large mixing bowl, mash the banana until chunky and not overly smooth.
Add the eggs, oil, vanilla extract, and sugar. Mix well.
In a separate bowl, combine oats, flour, baking powder, and salt. Add to wet mixture, and combine well. (Alternatively, simply add the dry ingredients on top of the wet ingredients and gently mix before incorporating them into the wet ingredients. This makes it a one-bowl recipe and this is how I make it.)
Add any optional add-ins.
Scoop the batter into a greased loaf pan, sprinkle with remaining oats, and bake for 45-60 minutes, or until fully cooked. A skewer will come out with a few moist crumbs but not wet batter. Check at 45 minutes and then keep baking and checking every 5 minutes until fully cooked through.
Let the loaf cool in the pan for 5 minutes and then move to a cooling rack to cool to room temperature before slicing.
Notes
Optional add-ins:
1/2 cup chocolate chips or chunks
1/2 cup chopped nuts or shredded coconut
1 teaspoon ground cinnamon
Tips
Use ripe bananas for this recipe but not too over-ripe. Using super overripe bananas makes the batter too liquid and the bread won't cook properly.
Mash the bananas only until they are mashed with some chunks. Use a fork or potato masher for best results. Over mashing the bananas to the point where they are liquid and smooth results in batter that's thin and bread that is too moist and dense. The batter doesn't bake properly and ends up being mushy in the center and sunken in the center after baking.
Let the bread cool completely before slicing to prevent it from crumbling.