Preheat oven to 350°F and spray a 9x5-inch loaf pan with nonstick cooking spray.
In a medium bowl, sift together flour, baking powder, baking soda, and salt. (Do not skip this step!) Set aside.
In a separate medium bowl, use a fork to mash the bananas and set aside.
In a stand mixer on medium-high, cream butter and sugar together for about 2 minutes, stopping to scrape the sides of the bowl as needed.
With the mixer on low speed, add eggs, one at a time. Add in buttermilk and vanilla until the batter is just combined (about a minute).
Slowly pour the flour mixture into the egg mixture, about ½ cup at a time. Mix on low until just combined.
Remove the bowl from the mixer and fold in the mashed bananas until evenly incorporated throughout the batter.
Pour the batter into the prepared pan and bake for 65-70 minutes, checking the bread at 50 minutes. The bread is done when a toothpick comes out mostly clean with a few crumbs, but no wet batter.