Preheat oven to 350F. Butter two 9-inch cake pans and line bottoms with parchment. Whisk flour, baking powder, and salt in a bowl. In a stand mixer, beat 10 tablespoons butter and sugar on medium-high until light and fluffy, about 4 minutes. Add eggs one at a time, beating well after each, then beat in vanilla. Reduce speed to low and add flour mixture in three additions alternating with milk in two additions, beginning and ending with flour. Mix just until smooth.

Divide batter between pans and smooth tops. Bake until golden and a toothpick comes out clean, 28 to 32 minutes. Cool in pans 15 minutes, then turn out onto wire racks to cool completely, about 1 hour.

In a medium saucepan off heat, whisk milk, sugar, cornstarch, and egg yolks until smooth. Cook over medium heat, whisking constantly, until mixture thickens and bubbles appear, 6 to 8 minutes. It should coat the back of a spoon. Remove from heat and whisk in butter and vanilla until glossy. Press plastic wrap directly onto surface and refrigerate until cold, at least 1 hour.

Place one cake layer on a serving plate. Spread half the pudding over top, leaving a 1/2-inch border. Press half the banana slices into pudding and sprinkle with 1/2 cup crushed wafers. Top with second cake layer, pressing gently to adhere. Repeat with remaining pudding, bananas, and another 1/2 cup wafers, leaving the top cake layer exposed.

Beat heavy cream, powdered sugar, and vanilla on medium-high until stiff peaks form, about 3 minutes. Frost top and sides of cake, creating swoops and swirls. Press remaining crushed wafers around the base and sprinkle a few on top for texture.

Refrigerate cake at least 2 hours or up to 8 hours to let flavors meld and pudding set. Slice with a sharp knife wiped clean between cuts. Serve cold for the true banana pudding experience.