Preheat oven to 350°F (180°C). Spray 2 (9-inch) round cake pans with baking spray with flour. Line bottom of pans with parchment paper.

In a large bowl, whisk together flour, sugars, baking powder, salt, baking soda, and cinnamon.

In a medium bowl, whisk together mashed banana, buttermilk, oil, eggs, and vanilla. Add banana mixture to flour mixture, and whisk until just combined. Divide batter between prepared pans (about 3½ cups or 1,000 grams each).

Bake until a wooden pick inserted in center comes out clean, 40 to 45 minutes. Let cool in pans for 10 minutes. Remove from pans, and let cool completely on a wire rack.

Level cooled cake layers, if desired. Place 1 cake layer on a serving platter. Spread 2 cups (415 grams) Browned Butter Frosting on top, spreading to edges with an offset spatula. Top with remaining cake layer. Spread remaining Browned Butter Frosting on top and sides of cake as desired, creating a slight border along top edge of cake. Refrigerate for at least 1 hour.

When ready to serve, top cake with Caramelized Bananas. Refrigerate in an airtight container for up to 3 days.