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For the cake:
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Preheat oven to 375F.
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Coat two 9-inch round cake pans with cooking spray and line the bottoms with wax paper or parchment paper.
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Whisk eggs, 1 cup sugar and oil in a large bowl.
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Add mashed bananas, buttermilk and 1 teaspoon vanilla.
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Stir whole-wheat flour, all-purpose flour, baking powder, baking soda and salt in a medium bowl.
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Add to the banana mixture and fold in just until blended.
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Divide the batter between the pans.
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Bake the cake until the tops spring back when touched lightly, 20 to 25 minutes.
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Let cool for 5 minutes, then turn out onto a wire rack and let cool completely.
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For the Bavarian cream:
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Place milk in a small saucepan, sprinkle gelatin over the milk and let stand for 1 minute to soften.
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Stir in 2 tablespoons sugar and heat over medium heat, stirring to dissolve the gelatin.
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Stir in 1/2 teaspoon vanilla and transfer to a medium bowl.
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Refrigerate, stirring occasionally, until the mixture has thickened to the consistency of raw egg whites, 40 to 45 minutes.
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Beat whipping cream until soft peaks form.
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Whisk one-third of the whipped cream into the milk mixture.
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Fold in the remaining whipped cream.
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Refrigerate until set and thickened to the consistency of whipped cream again, about 1 hour.
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To assemble cake:
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Shortly before serving, place 1 cake layer on a serving plate and spread half the Bavarian cream over it.
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Peel and slice the remaining bananas; arrange half the slices evenly over the cream.
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Top with the second cake layer.
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Spread the remaining cream over the cake and arrange the remaining banana slices decoratively over the top.
