Preheat the oven to 180C (350F) and grease a loaf pan (26x13centimeters)(10x5 inches)
In a large bowl, mix together the banana, melted butter, eggs, sugar, and vanilla.
Add the rest of the ingredients, and mix with a ladle until well incorporated.
Pour the batter in the prepared pan. If desired, sprinkle 2 tablespoons oats on top. Bake for 45 to 50 minutes, or until the center of the bread is cooked (insert the tip of a knife and it should come out clean).
Leave in the pan for 15 minutes before removing to a cooling rack.
Let cool completely and serve.