Heat the oven to 350°F and arrange a rack in the middle. Coat a 9-by-5-inch loaf pan with butter and dust it with flour, tapping out the excess. Whisk together the measured flour, baking powder, salt, baking soda, and cinnamon in a large bowl to aerate and break up any lumps. Set aside.
Place the sugar, eggs, oil, and vanilla in the bowl of a stand mixer fitted with a paddle attachment and beat on medium speed until thoroughly combined, about 2 minutes. Add the bananas and sour cream and mix until just combined. Scrape down the sides of the bowl, add the flour mixture, and mix until just combined.
Turn the batter into the prepared loaf pan and bake until a toothpick inserted in the center comes out clean, the top is golden brown, and the bread is pulling away from the sides of the pan, about 1 hour.
Transfer to a wire rack to cool for 10 minutes. Slide a knife around the perimeter of the pan, invert to release the bread, and cool completely on the wire rack before serving.