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1
: In a large saucepan with high sides, combine the sugar and 1/3 cup of water. Stir the mixture gently so you don't splash any of it up on the sides of the pan. Turn the heat to medium-high and continue stirring until the sugar dissolves. Increase the heat to high, stop stirring, and allow the mixture to boil. Once it begins to turn a rich caramel color, remove it from the heat and gently stream in the cream (it will bubble up, so add the cream slowly at first). Stir until combined. Set aside.
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2
: In a medium bowl, whisk the eggs and egg yolks until pale and blended.
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3
In another medium bowl, whisk together 1 cup of the half-and-half, the cornstarch, and the salt until the mixture is uniform and the cornstarch has dissolved. Whisk this mixture into the caramel base.
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4
Place the caramel mixture over medium-high heat and whisk in the remaining 3 cups of half-and-half. While whisking constantly but gently, bring the mixture to a boil, reduce the heat to medium, and boil (still whisking) for about 15 seconds. The mixture will thicken. Remove from the heat and continue whisking vigorously for about 15 seconds to release excess heat.
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5
Pour one-third of the caramel mixture into the egg mixture, whisking the egg mixture constantly. Transfer the egg mixture into the saucepan with the caramel mixture and, whisking constantly, bring back to a boil. Cook for 1 to 2 minutes, until the custard is very thick. Remove from the heat and whisk in the butter, then the vanilla bean paste.
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6
Push the custard through a fine-mesh sieve into a separate bowl and allow the custard to come to room temperature, about 1 hour. Stir the custard, cover the bowl, and place in the refrigerator for about 1 hour to chill. (The custard can be made up to 24 hours ahead of time and should be stored in the refrigerator, tightly covered.)
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7
: Thirty minutes before the custard is entirely chilled, place eight 6-ounce ramekins or a large 11/2-quart souffle or baking dish on a baking sheet and use one of the following methods for assembling the final dish, then return the pudding, uncovered, to the refrigerator to chill while you make the meringue topping.
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8
Spread a small amount of pudding on the bottom of each ramekin or of the large dish. Thinly slice the bananas and arrange in a single layer on top. Sprinkle one-third of the cookies on top of the bananas, then cover with one-third of the remaining pudding. Repeat twice more (bananas, cookies, pudding) so that your top layer is pudding.
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9
Thinly slice the bananas and sprinkle them over the chilled pudding. Sprinkle the cookies over the bananas. Using a wooden spoon, fold the bananas and cookies into the pudding until completely combined. Divide the mixture equally among the ramekins or pour into the large dish.
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10
: Preheat the oven to 350u00b0F.
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11
Place the egg whites in the bowl of a standing mixer fitted with the whisk attachment, and sprinkle them with the cream of tartar. Beat on medium-high speed until soft peaks just begin to form, 4 to 5 minutes. Reduce the speed to medium, slowly stream in the sugar, and continue beating until the whites are glossy and stiff but not dry.
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12
Pile the meringue high and with a little artistic flair directly onto the pudding. Be sure to spread it all the way to the edges.
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13
Bake for 12 to 15 minutes or until the meringue turns golden brown. Place the sheet pan with the pudding on a wire rack to cool for 30 to 40 minutes.
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14
Banana pudding tastes great slightly warm (though it will be very runny) and even better thoroughly chilled. It can be stored in the refrigerator, tightly covered, for up to 3 days; note that the cookies will continue to soften as time goes on.
