Heat oven to 350ºF. Coat a 9-by-5-inch loaf pan with nonstick spray and set aside.
Spread oats into a thin layer on a half-sheet pan and bake until lightly toasted, about 15 minutes. Remove pan and cool oats 2 to 3 minutes.
Grind oats in a food processor until the consistency of whole wheat flour, about 3 minutes. Then pulse in the flour, baking soda, baking powder, and salt.
Cream the butter and sugar in a stand mixer fitted with the paddle attachment on medium speed until pale and fluffy, about 3 minutes.
Drop speed to low and add eggsAdd those eggs slowly so that the water and fat phases have time to come together., one at a time, incorporating each fully before adding the next. Stop to scrape down the sides of the bowl, if necessary.
Follow with the vanilla and banana, and beat on medium-low speed until incorporated. The batter will look kind of curdled, but that’sOK.
Add the flour mixture and beat on low speed until just combined.
With the mixer on the lowest speed, slowly add the flour mixture until just combined. Scrape down the sides of the bowl as needed.
Transfer the batter to the prepared pan and bake until the internal temperature reaches 200 to 210ºF, 50 to 55 minutes.
Cool pan on a wire rack for 15 minutes before turning the loaf out and cooling completely.