Step 1

Prepare the Cake: Preheat oven to 350°F. Coat a 13- x 9-inch baking pan with cooking spray. Sift together flour, baking powder, cinnamon, salt, and baking soda in a medium bowl. Set aside.

Step 2

Beat sugar, eggs, oil, buttermilk, and vanilla in a large bowl with an electric mixer on medium speed until combined, about 2 minutes. Add flour mixture to sugar mixture, one-third at a time, and beat on low speed just until smooth after each addition. Fold in mashed bananas, and transfer batter to prepared pan.

Step 3

Bake in middle of preheated oven until a wooden pick or cake tester inserted in center of cake comes out clean, 30 to 35 minutes. Transfer to a wire rack, and cool 10 minutes. Using the handle of a wooden spoon, poke deep holes all over the cake (about 5 across and 6 down, for a total of 30 holes).

Step 4

Prepare the Pudding: Whisk together sugar, cornstarch, and salt in a large saucepan; whisk in milk. Whisk in egg yolks until well blended. Bring to a boil over medium, stirring constantly. Immediately reduce heat to low, and simmer, stirring constantly, just until pudding is thick enough to coat the back of a spoon, 1 to 2 minutes.

Step 5

Pour pudding through a fine wire-mesh strainer into a large bowl. Whisk in vanilla bean paste and butter. Cool, stirring occasionally, until lukewarm, about 15 minutes. Spread pudding evenly over cake. Cover cake with plastic wrap, pressing it directly onto pudding (to prevent a skin from forming). Chill the cake for at least 2 hours but preferably overnight.

Step 6

Preheat oven to 350°F. Remove plastic wrap from cake. Scatter banana slices evenly over pudding. Beat heavy cream, powdered sugar, and vanilla in a large bowl with an electric mixer on medium-high speed until thick and spreadable. Spread over bananas, covering cake in an even layer.

Step 7

Stir together crushed vanilla wafers, melted butter, flour, and granulated sugar in a small bowl. Press mixture with your fingers to form small clumps, and spread on a baking sheet. Bake in preheated oven until crisp and brown, 5 to 6 minutes. Cool completely, about 10 minutes. Sprinkle over whipped cream topping. Serve immediately.