With the rack in the center of the oven, preheat to 325°F. Lightly oil and flour a standard 9x5 loaf pan. Sift together the flour, baking powder, baking soda, cinnamon and salt in a bowl and set aside.
With a stand mixer fitted with the whip attachment, beat together the sugar and eggs on medium speed until light and fluffy, about 5 minutes. Switch to low speed and slowly drizzle in the oil, taking your time.
Add the bananas, sour cream, and vanilla, and continue to mix on low speed just until combined.
Use a rubber spatula to fold in the flour mixture until thoroughly combined. No flour streaks should be visible.
Pour the batter into the prepared loaf pan and bake for 1 to 1 1/4 hours. The banana bread should be golden brown on top and will spring back when you press it.
Let cool in the pan on a wire rack for 30 minutes, remove from the pan and let cool completely on the wire rack. Enjoy!