Preheat the oven to 350º F (180º C). Using a baking spray, generously grease the cake pan(s). For a 2-layer cake, you can bake this cake in two 4, 5, or 6-inch cake pans, or in a 9x13-in rectangular pan and cut the circle as I show in the photos above (see notes for more details).
In a large bowl, whisk together flour, baking powder, baking soda, and salt. Set aside.
In a mixing bowl, combine milk and vinegar. Let the mixture stand at room temperature for 5 -8 minutes. When it is ready, the milk will be slightly thickened, and you will see small curdled bits. Reserve.
In a large bowl, beat butter until creamy on medium-high speed for about 3 minutes. Scrape down the sides and up the bottom of the bowl with a rubber spatula as needed. Add maple syrup mashed banana and vanilla; continue beating to combine.
Reduce speed to low and add half of the flour mixture. Scrape down the mixing bowl with a spatula and turn the batter over several times to ensure all of the ingredients are well incorporated. Add milk mixture; continue beating to incorporate. Add the remaining flour; beat just until combined. Do not overmix this batter.
Pour the cake mixture into the prepared pan(s). Bake until a skewer comes out clean when poked in the center. Baking times will vary, depending on what kind of pan you use, so keep an eye on yours. The cake is done when a toothpick inserted in the center comes out clean. For 2 small round cake pans bake for about 18-21 minutes. For a 13x9 rectangular pan bake for 20-25 minutes.
Allow cake to cool completely in the pan set on a wire rack. The cake must be completely cool before frosting.