1. Make cake: Preheat oven to 350ºF. Grease 3 9-inch round cake pans and line bottoms with parchment. Sift flour, baking powder, baking soda and salt together into a small bowl. In a large bowl, using an electric mixer on medium-high speed, beat butter and sugar until light, about 3 minutes. Beat in maple syrup. Add eggs 1 at a time, beating well after each. Scrape down sides of bowl.
2. Reduce mixer speed to low. Beat in half of flour mixture until nearly combined, then buttermilk, then remaining flour mixture. Do not overmix. Beat in extract. Fold in bananas. Divide batter among pans; bake until a toothpick inserted into center comes out clean, 25 to 30 minutes. Let cakes cool in pans on a wire rack for 10 minutes, then turn cakes out onto rack, remove parchment and let cool completely.
3. Make frosting: In a large bowl, using an electric mixer on medium-high speed, beat cream cheese and butter until combined. Reduce mixer speed to medium-low and gradually beat in sugar. Add extract and beat until smooth.
4. Assemble cake: Put 1 layer on a cake platter and spread 1/3 of frosting on top. Lay 1/2 of banana slices over frosting. Repeat. Put third layer on top and spread remaining 1/3 of frosting on top. Chill 1 hour to allow frosting to set. Just before serving, drizzle with caramel sauce, if desired.