Pour the milk into a medium saucepan and place over medium heat. Heat until bubbles form around the edges.
Whisk together the sugar, cornstarch, and egg yolks in a large bowl. Add a little of the hot milk to the sugar mixture, whisking constantly. Add the remaining milk until all is incorporated, whisking constantly.
Wipe out the saucepan. Strain the mixture through a fine wire-mesh strainer into the cleaned saucepan. Cook, whisking constantly until the mixture coats the back of a wooden spoon. Transfer to a clean bowl and whisk in the butter and vanilla. Cover the surface of the pudding with a piece of plastic wrap to prevent a skin from forming. Let cool completely.
Make the whipped cream: Beat the cream cheese, powdered sugar, and vanilla with a handheld mixer in a large bowl until smooth. Add the whipped cream and beat until stiff peaks form.
Layer the pudding, bananas, cookies, and whipped cream in Mason jars or small dessert cups, layering twice and ending with whipped cream. Refrigerate for at least 2 hours or until ready to serve. Garnish the tops with more cookies and banana slices, if desired.