Walnuts and bananas are a good combination in any presentation, but work especially well in this tart, where the walnut filling covers the bananas, which bake to a sweet, jam-like consistency.
Set a rack in the lowest level of the oven and preheat to 350°F (180°C).
For the filling, pulse the walnut pieces and brown sugar in a food processor fitted with the metal blade until the nuts are finely ground. Add the butter, egg, egg yolk, cinnamon, vanilla, flour, and baking powder. Pulse to make a thin batter.