Preheat your oven to 375°F, and grease an 8" or 9" bread pan well. We like to use coconut oil for this.
Place peeled bananas in a medium-sized mixing bowl. Using a fork, mash bananas into a puree. Add applesauce, olive oil, egg, and vanilla extract, and mix well.
In another bowl, combine the rest of the ingredients (flour, sugar, baking soda, and salt). Mix well and then add to the banana mixture.
Once the batter is well-mixed, pour it into the pre-oiled bread pan.
Bake for ~45 minutes at 375°F. The top will look browned, and a knife or toothpick should come out clean.