Position a rack in the center of the oven and preheat to 325°F. Generously spray the bottom and sides of a 9 x 13-inch cake pan with cooking spray.
In a medium bowl, whisk together 2 ⅔ cups all-purpose flour, 1 ½ teaspoons baking powder, 1 teaspoon baking soda, and 1 teaspoon kosher salt.
In the bowl of a stand mixer fitted with a paddle attachment, combine ¾ cup unsalted butter and 2 cups granulated sugar. Beat on medium-high for 2 to 3 minutes, or until light, fluffy, and doubled in volume, scraping down the bottom and sides of the bowl with a rubber spatula as necessary. Reduce the mixer to low and add 2 large eggs, one at a time, only adding the next egg when the previous one is incorporated and scraping down the bottom and sides of the bowl after each addition. In a liquid measuring cup, whisk together 1 cup buttermilk, ¼ cup canola oil, and 1 teaspoon pure vanilla extract. With the mixer on low, pour in the liquid ingredients. Increase the mixer to medium-high and beat for 5 minutes, or until the mixture is practically white in color and doubled in volume. Scrape down the bottom and sides of the bowl.
With the mixer on low, add 2 cups mashed bananas a heaping spoonful at a time. Beat for 1 minute, until the bananas are broken up and evenly distributed throughout the mixture. Gradually add the dry ingredients (from the 2nd step) and beat until just combined. Scrape down the bottom and sides of the bowl one last time, and beat for an additional 30 seconds to incorporate any stuck ingredients.
Pour the batter into the prepared pan and bake for 55 to 65 minutes, or until the top of the cake is golden, slightly puffed, and a skewer inserted into the cake comes out with few crumbs attached. Cool on a wire rack for 20 minutes, then use the wooden skewer to poke the entire surface of the cake with many deep holes that reach the bottom of the pan. Cool completely before soaking and assembling.