Line the bottom of a 9x13-inch dish with a single layer of shortbread cookies.
In a large bowl, beat the softened cream cheese and sweetened condensed milk until completely smooth. Stir in the flaky sea salt and vanilla paste. The salt is the "secret" that keeps this dessert from being cloying.
In a separate bowl, whisk together the milk and the French vanilla pudding mix for 2 minutes. Once set, fold the pudding into the cream cheese mixture.
Gently fold in the whipped topping (or fresh whipped cream) until the mixture is light, airy, and free of streaks.
Place a layer of sliced bananas directly on top of the cookies. Pour half of the pudding mixture over the bananas. Repeat with another layer of bananas and the remaining pudding.
Arrange the second bag of shortbread cookies in neat rows across the top of the pudding.
While 4 hours is the minimum chill time, letting this sit for 12–24 hours is preferred. This allows the cookies to soften into a cake-like texture while the bananas slightly macerate into the cream.