Preheat your oven to 180°C (356°F) and grease and line a 2lb loaf tin.
In a small saucepan over medium heat, melt the butter and set aside to cool.
In a medium mixing bowl, combine the vegetable oil, caster sugar, brown sugar, and eggs. Add 2 of the bananas (broken into chunks), the melted and cooled butter, and the Greek yogurt. Mix well using a fork or wooden spoon.
Sift the flour directly into the bowl and stir in the bicarbonate of soda and salt. Mix until just combined.
Fold in the chocolate chips or chunks, reserving 2 tablespoons for sprinkling on top.
Pour the batter into the prepared loaf tin. Slice the remaining banana lengthwise and place it on top of the batter. Sprinkle with the reserved chocolate chunks.
Bake in the preheated oven for about 40 minutes, or until a skewer inserted into the center comes out with only a couple of moist crumbs.
Allow the bread to cool in the tin for 10 minutes before transferring it to a wire rack to cool completely.