Preheat the oven to 350ºF. Mash the bananas in a large bowl. Add the eggs, butter, 1/4 cup oil, vanilla and sugar. Stir to combine thoroughly.
In a separate large bowl, mix flour, baking soda and salt. Add banana mixture to flour, stirring to combine. A silicone spatula does a great job. Fold in the chopped nuts.
Grease a 5×9-inch glass baking dish with a little oil. Pour the batter into the baking dish and bake in center of the oven until a wooden pick inserted in the middle of the bread comes out clean, about 1 hour (check at 50 minutes—ovens vary).
Cool for 15 minutes on a wire rack, then work around the outside edges of the bread with a thin, flexible metal baking spatula and turn the bread out onto the rack to cool completely. Serve at room temperature. Or, if you're impatient as we were, cut into it while it's still warm.