Preheat the oven to 350°F. Grease two 9-inch round cake pans, line with parchment paper rounds, then grease the parchment paper.
Mash the bananas.
In a medium bowl, whisk together the oat flour, almond flour, baking powder, baking soda, cinnamon, and salt.
In a large bowl, cream the butter and brown sugar using a mixer on high speed until smooth, about 2 minutes. Scrape down the sides and up the bottom of the bowl with a rubber spatula as needed. Add the eggs and the vanilla and beat on medium-high speed until combined.
Beat in the mashed bananas, scraping down the bowl as needed. With the mixer on low speed, add the dry ingredients in three additions alternating with the buttermilk and mixing each addition just until incorporated.
Divide batter evenly between the two pans. Bake for 35-40 minutes, checking at 30 minutes, until a tester inserted in the middle of the cake comes out clean and the sides are starting to come away from the edges of the pan.
Remove the cakes from the oven and set on a wire rack. Allow to cool completely in the pan.
Remove the cake from the pans and chill in the fridge for at least 1 hour or up to overnight before frosting.