Line bottom of 9 by 13-inch baking pan with half of shortbread cookies followed by all of the bananas slices.
In small bowl, combine milk and pudding mix and whisk until smooth. Cover with plastic wrap and refrigerate until ready.
In bowl of stand mixer, whip heavy cream using whisk attachment until soft peaks form. Slowly add powdered sugar and vanilla extract and continue to whip until stiff peaks form. Scrape from bowl and place into another container and refrigerate until needed.
In same bowl used for whipping cream, using same whisk attachment, whip cream cheese until smooth. Slowly add sweetened condensed milk and continue to whip until smooth and combined.
Fold whipped cream into cream cheese mixture, followed by pudding mixture.
Spread onto bananas in pan. Top with the rest of the cookies. Cover and set in refrigerator for at least 4 hours, preferably overnight. Cookies should become soft after sitting long enough.