Heat the oven to 350°F (175°C). Grease a 9x5-inch loaf pan and line it with parchment paper, leaving an overhang on the long sides.
In a large bowl, mash the bananas with a fork until mostly smooth.
Whisk in the oil, melted butter and brown sugar until combined.
Add the eggs, sour cream and vanilla and whisk until smooth and glossy.
Sprinkle the flour, baking soda, salt and cinnamon over the wet ingredients. Fold gently with a spatula until just combined, with a few small streaks of flour still showing.
Fold in the chocolate chips or walnuts, if using.
Pour the batter into the prepared pan and smooth the top. Sprinkle with coarse sugar.
Bake for 55 to 65 minutes, until the top is deep golden and a toothpick inserted in the center comes out with a few moist crumbs. If the top browns too quickly, loosely tent the loaf with foil after 40 minutes.
Cool in the pan for 15 minutes, then lift out and cool on a wire rack for at least 30 minutes before slicing.