Prepare the Shortcut Salted Caramel: Melt butter and light brown sugar in a small saucepan over medium, stirring occasionally. Stir in dulce de leche. Bring to a boil, stirring constantly, until smooth, about 2 minutes. Remove from heat, and stir in cream and salt. Cool 10 minutes.
Prepare the Custard: Whisk together granulated sugar, flour, and salt in a large, heavy saucepan. Whisking constantly, add whole milk in a slow, steady stream. Whisk in egg yolks. Cook over medium-high, stirring continuously with a rubber spatula, until it bubbles around the edges and coats the spatula, 8 to 10 minutes. Remove from heat, add butter, and stir until it melts. Stir in vanilla extract. Press plastic wrap directly on surface to prevent a skin from forming, and cool completely, about 1 hour.
Prepare the Whipped Cream: Beat heavy cream with an electric mixer on medium-high speed until foamy; gradually add powdered sugar, beating until soft peaks form.
Assemble the pudding: Cover bottom of a 2-quart baking dish or serving bowl with 14 cookies, breaking them as needed. Drizzle with half of the Shortcut Salted Caramel; top with half of the sliced bananas and half of the Custard. Repeat layers with remaining cookies, caramel, bananas, and Custard. Spread Whipped Cream on top, and chill 30 minutes before serving.