In a mixing bowl, whisk together flour, baking powder, sugar and salt; set aside.
In your mixer's bowl, beat the egg yolks for 4 to 5 minutes on high speed, or until lemony yellow.
With the mixer on low, add apple juice and vanilla.
Slowly add the melted butter and continue to mix until combined.
Gradually add in the flour mixture, about 1/4-cup at a time; continue to mix until thoroughly incorporated.
Remove bowl from mixer and set aside.
In a clean, dry mixing bowl, beat the egg whites on medium-high speed until stiff peaks form.
Using a rubber spatula, gently fold the egg whites into the flour mixture. (***see notes)
Spoon dollops of the cake batter over the bananas and using an offset spatula, gently spread the batter, covering the fruit.
Set a baking sheet on the bottom of the oven.
Bake the cake in the center of the oven for 25 to 30 minutes, or until a toothpick inserted into the center comes out clean.
Remove from oven and let the cake cool in the pan for 10 minutes.
Invert it onto a platter.
Let the cake cool slightly; about 20 minutes.
Cut into squares and serve.