Prep your oven and pan. Position a rack in the center of the oven and preheat the oven to 350°F. Spray a 9 x 5-inch loaf pan with cooking spray and line with parchment paper, leaving a 2-inch overhang on the long sides. Spray the parchment, too.
Make the banana bread. In a medium bowl, whisk together the flour, baking soda, and salt.
In the bowl of a stand mixer fitted with the paddle attachment, combine the butter and brown sugar. Beat on medium-high until light, fluffy, and doubled in volume, 3 to 5 minutes, using a rubber spatula to scrape down the bottom and sides of the bowl as necessary. Reduce the mixer to low and add the eggs one at a time, adding the next egg only after the previous one has been fully incorporated, scraping down the bottom and sides of the bowl after each addition. Add the sour cream and vanilla all at once and beat on low until combined. Gradually add the dry ingredients and beat until just combined. Add the bananas a handful at a time and beat until broken into pieces and distributed evenly throughout the batter, about 1 minute. Scrape down the bottom and sides of the bowl once more, and beat on low for an additional 30 seconds. Pour the batter into the prepared pan and use an offset spatula to smooth the top. Use a sharp knife to slice an extra peeled banana (there's no need to weigh this one!) in half lengthwise. Place the banana halves, cut-side up, on top of the batter. Bake the banana bread. Bake for 60 to 65 minutes, or until a skewer inserted into the center of the banana bread comes out with few crumbs attached. Cool on a wire rack.
Serve and store. Serve warm or at room temperature. The banana bread can be stored at room temperature, wrapped tightly in plastic wrap, for up to 3 days.