Place 2 cups cold milk and 2 (3.4-ounce) boxes instant vanilla pudding in a large bowl. Beat with an electric hand mixer on medium speed until completely smooth, about 15 seconds. Add 1 (14-ounce) can sweetened condensed milk and a pinch of kosher salt. Blend on medium speed until smooth. Press a sheet of plastic wrap directly onto the surface of the pudding. Refrigerate until the pudding is firm, at least 1 hour or up to overnight.

Once the pudding is set, make the whipped cream. Place 2 cups cold heavy cream in a large bowl. Beat with an electric hand mixer on medium speed, scraping down the sides and bottom of the bowl about halfway through, until stiff peaks form, about 3 minutes total.

Remove the pudding from the refrigerator and stir to loosen. Add ⅔ of the whipped cream (about 2 ½ cups) and gently fold together. Add 1 teaspoon vanilla bean paste or vanilla extract and 1 tablespoon powdered sugar to the remaining whipped cream and gently fold to combine; cover and refrigerate until ready to use.

Peel 4 large barely ripe bananas and cut crosswise into ¼-thick slices. Set aside 5 vanilla wafer cookies for topping. Spread ¼ of the pudding in an even layer in a serving bowl. Arrange ⅓ of the remaining vanilla wafer cookies on top, followed by ⅓ of the banana slices.

Repeat layering pudding, vanilla wafer cookies, and banana slices two more times. Top with the remaining pudding. Dollop the whipped cream over the top and spread into an even layer. Cover and refrigerate for at least 4 or up to 12 hours. Crush the 5 reserved cookies and sprinkle over the pudding just before serving.