Preheat the oven to 350°. Place ten 4-inch fluted tartlet pans with removable bottoms on a baking sheet. Spray the pans with vegetable oil spray.
In a medium bowl, combine the ground almonds with the flour, butter, rum, vanilla and 2/3 cup of the sugar. Fold in the chopped bananas.
In a large bowl, beat the egg whites with the salt at high speed until frothy. Slowly pour in the remaining 2/3 cup of sugar and beat until stiff peaks form.
Using a rubber spatula, fold the beaten whites into the almond batter, 1 cup at a time. Spread the batter evenly in the prepared pans and bake for about 20 minutes, or until golden and firm in the centers. Meanwhile, slice the 4 remaining bananas 1/4 inch thick on the diagonal.
Unmold the cakes. Set each one in the center of a dessert plate and cover with the sliced bananas. Pour the Warm Caramel Sauce on top and serve.