Preheat the oven to 350F.

Butter two 9-by-2-inch round cake pans and line bottoms with parchment paper.

Butter the parchment paper and dust with flour, tapping out any excess.

Sift together flour, baking powder, baking soda, and salt in a medium bowl.

In a small bowl, mix mashed bananas, sour cream, and vanilla extract.

Beat butter and 1 2/3 cups sugar on medium-high speed until light and fluffy.

Add eggs one at a time, beating well after each addition.

Add the flour mixture in two parts on low speed, beating until combined after each addition.

Fold in the banana mixture using a rubber spatula.

Divide the batter between the prepared pans.

Bake for 30 to 35 minutes, rotating the pans halfway through, or until a cake tester comes out clean.

Cool in the pans on a wire rack for 20 minutes.

Invert the cakes onto the rack and peel off the parchment paper.

Reinvert the cakes and let them cool completely, top sides up.

Sprinkle 1/4 cup sugar into a large skillet and cook over high heat until caramelized.

Remove from heat and stir in 3 tablespoons of butter until melted.

Return the pan to medium heat and add sliced bananas.

Cook the bananas until they start to brown, about 1 to 2 minutes.

Gently turn the bananas and cook until browned, about 2 minutes more.

Trim the tops of the cake layers to make them level.

Place one layer on a cake plate and arrange caramelized banana slices on top.

Place the remaining layer on top.

Spread Mascarpone Frosting over the entire cake, swirling to cover completely.

Drizzle Caramel Sauce over the top of the cake, or serve alongside each slice.

Serve immediately, or refrigerate for up to 3 days.

To make Mascarpone Frosting: Beat mascarpone cheese, heavy cream, and confectioners sugar until medium-soft peaks form.

Use immediately.

To make Caramel Sauce: Prepare an ice bath.

Cook sugar in a medium saucepan over medium-high heat until it starts to melt around edges.

Continue to cook, stirring, until golden amber, about 3 minutes.

Remove from heat and add cream in a slow, steady stream, stirring constantly.

Return pan to heat briefly if needed, stirring until the mixture is smooth.

Place caramel in a bowl in the ice bath and let stand until cold, stirring frequently.