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Mash the bananas until smooth.
In a saucepan, whisk egg yolks, sugar, and cornstarch. Gradually add milk while stirring.
Cook over low heat, stirring constantly until thickened.
Remove from heat and add mashed banana, butter, and vanilla extract. Mix well.
Cool completely, cover, and refrigerate until ready to use.
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Whisk eggs and sugar until pale and fluffy.
Add milk, vegetable oil, and vanilla extract; mix gently.
Fold in sifted flour carefully.
Pour batter into lined molds or pipe oval shapes on a tray.
Bake at 170°C (340°F) for 10–12 minutes. Let cool completely.
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Cut the sponge into oval shapes.
Pipe banana custard onto the center of each piece.
Fold gently to form the classic Tokyo Banana shape.
Chill briefly before serving.