Heat the oven to 350°F (180°C) with a rack in the center. Butter a 9x5-inch loaf pan, dust it with flour, and tap out the excess. You can line it with a parchment sling instead, which lets the cake lift out cleanly.
Butter and flour for the pan
Sift the flour, baking powder, baking soda, cinnamon, and salt into a medium bowl. Whisk to combine and set aside.
2 ½ cups all-purpose flour (310 g ), 2 teaspoons baking powder , ½ teaspoon baking soda (3g), ½ teaspoon ground cinnamon, ¼ teaspoon fine salt
In a large bowl, mash the bananas with a fork until mostly smooth, with a few small lumps left. Whisk in the sugar for about 1 minute, until it starts melting into the banana. Add the oil, eggs, and vanilla and whisk until smooth and glossy.
3 large very ripe bananas, ¾ cup plus 2 tablespoons, granulated sugar (180g), ½ cup vegetable oil (100g), 2 large eggs, 1 teaspoon vanilla extract
Add the flour mixture. Fold with a rubber spatula just until no dry streaks remain. The batter will be thick. Scrape it into the prepared pan and smooth the top.
Bake 50 to 60 minutes, until the top is deep golden and springs back when pressed, and a toothpick in the center comes out clean or with a few moist crumbs. Start checking at 45 minutes. If the top browns too fast, tent it loosely with foil around the 35-minute mark.
Cool in the pan on a rack for 10 minutes. Run a knife around the edges, turn the cake out, and let it cool completely, about 1 hour, before slicing.