Preheat the oven to 325 degrees F. Make the filling: Beat the cream cheese and vanilla in a stand mixer fitted with the paddle attachment on medium speed until smooth; transfer to a bowl. Clean out the mixer. Add the egg whites to the mixer and beat with the whisk attachment on medium-high speed until frothy, about 1 minute. Gradually beat in the sugar, then increase the mixer speed to high and beat until shiny, stiff peaks form, about 3 minutes. Add half of the cream cheese mixture and beat until just combined. Add the remaining cream cheese mixture and beat until smooth. Transfer the filling to a pastry bag fitted with a large round tip; set aside.
Make the cakes: Line a 12-cup muffin pan with paper liners. Sift the flour, baking soda and salt into a bowl.
Clean out the mixer. Beat the butter, sugar and vanilla with the paddle attachment on medium speed until fluffy, about 5 minutes. Beat in the eggs, one at a time. Beat in the mashed bananas until combined. Add half of the flour mixture and beat on low speed until almost combined, then add the remaining flour mixture and beat until just combined (do not overmix).
Divide the batter among the prepared muffin cups. Insert the pastry tip halfway into each and pipe about 1 tablespoon filling into the middle of the batter. (The cups should be about three-quarters full.) Bake until a toothpick inserted into the cake (not the filling) comes out clean, 20 to 35 minutes. Transfer the pan to a rack and let cool about 15 minutes, then remove the cakes to the rack to cool completely.