Preheat the oven to 350F (180C). Lightly grease a 10"x15"x1" jelly roll pan, then dust with flour. Set aside.
In a medium bowl, whisk together the flour, cinnamon, baking soda and salt. Set aside.
In a separate large bowl, beat together the butter, granulated sugar and brown sugar until creamed.
Mix the eggs and vanilla into the butter mixture until you no longer see pieces or lumps of egg.
Mix the sour cream and mashed bananas into the butter mixture. Note: Be sure to cut any bruises out of the bananas before mashing. Mash the bananas well, then measure. If there are lumps in your batter from the bananas - that's OK.
Add the dry ingredients to the bowl and mix them into the batter, starting with the mixer on a low speed or using a wire whisk. I typically do this about 1/2 at a time. When you're finished, there shouldn't be lumps of flour but a lumpy mixture due to the bananas is OK and expected.
Pour the batter into the prepared pan and smooth into an even layer.
Bake in the preheated oven for about 24-28 minutes, or until the top is golden, an inserted toothpick comes out clean or with a few moist crumbs, and the bars are starting to pull away from the edges of the pan.