Banana Pudding Cake

Prepare the Filling: Whisk together sugar, cornstarch, and salt in a heavy saucepan. Whisk together egg yolks and half-and-half in a bowl; gradually whisk into sugar mixture. Cook over medium, whisking constantly, until mixture just starts to bubble, 6 to 7 minutes. Cook, whisking constantly, 1 more minute; remove from heat. Whisk in butter and vanilla until completely incorporated; transfer to a medium bowl. Place plastic wrap directly on warm filling to prevent film from forming. Let stand 30 minutes; chill 4 to 24 hours.

Meanwhile, prepare the Cake Layers: Preheat oven to 350°F. Beat butter with a heavy-duty stand mixer fitted with paddle attachment on medium speed until creamy. With mixer running on medium speed, gradually add sugar, beating until light and fluffy, about 2 minutes. Add eggs, 1 at a time, beating just until blended after each addition. Stir in vanilla.

Stir together cake flour, baking powder, and salt in a bowl. Add flour mixture to butter mixture alternately with milk, beginning and ending with flour mixture. Beat on low speed just until blended after each addition. Spoon batter into 3 greased (with shortening) and floured 8-inch round cake pans.

Bake in preheated oven until a wooden pick inserted in center comes out clean, 19 to 23 minutes. Cool in pans on wire racks 10 minutes. Remove from pans to wire racks, and cool completely, about 1 hour.

Beat heavy cream with an electric mixer on high speed until stiff peaks form. Gently fold whipped cream into chilled custard Filling.

Assemble cake: Horizontally slice a very thin layer off the top of each Cake Layer with a serrated knife (to remove any dome). Place 1 Cake Layer, cut side up, on a serving platter; cover Cake Layer with half of sliced bananas. Spread about 1 1/2 cups Filling over top of bananas. Top with second Cake Layer, cut side up; repeat with remaining bananas and 1 1/2 cups Filling, ending with remaining Cake Layer, cut side down. Spread top and sides of cake with Vanilla Whipped Cream Frosting.

Crush 20 vanilla wafers in a ziplock bag, and press crushed wafers gently around bottom of cake (about 2 to 3 inches up the sides). Garnish top of cake with whole vanilla wafers.