Bring the milk and vanilla beans to a simmer in a medium saucepan over low heat. Using tongs, remove the beans from the milk. Using the tip of a small sharp knife, scrape the tiny seeds from each bean back into the milk.

Whisk the Sugar, cornstarch and salt in a medium bowl. Add the egg yolks and whisk well. Gradually whisk in about half of the hot milk, then pour the yolk mixture into the saucepan. Cook over medium heat, stirring constantly, until the pudding comes to a full boil. Remove from the heat and whisk in the butter until melted. Transfer to a medium bowl. Cover the pudding with a piece of plastic wrap pressed directly onto the surface and pierce a few holes in the wrap with the tip of a knife. Let stand until tepid, about 30 minutes.

Spoon about 1 cup of the pudding into a 2- to 2 1/2-quart glass bowl. Layer the cookies, bananas and pudding in the bowl, ending with the pudding. Cover tightly and refrigerate until chilled, at least 4 hours or overnight.

Whip the cream and confectioners' Sugar in a chilled medium bowl until stiff. Spread the whipped cream over the pudding. Serve chilled, spooned into bowls.

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