Whisk the cornstarch, sugar, egg yolks and salt in a medium bowl. Heat the milk, half-and-half, and mashed banana in a medium saucepan over medium heat until bubbles form around the edges. While whisking the egg yolks, add the hot milk a little at a time. When the bowl feels warm, whisk in the remaining milk. Make sure you whisk well.
Return to the saucepan and set over medium heat. Whisk until the custard thickens and then boils for 2 minutes. Put the vanilla and butter in a large bowl and strain the hot cream over them through a fine-mesh sieve. Stir until smooth, then press a piece of plastic wrap directly on the surface and refrigerate until cold.
Whisk the cream in a large bowl until soft peaks form. Whisk one third of the whipped cream into the pastry cream to loosen it, then gently fold the remainder until incorporated. Fold in the banana chucks.
For the Meringue
Whisk the egg whites and the sugar in the bowl of an electric mixer set over a saucepan of simmering water until the sugar dissolves and the mixture is warm to the touch. Immediately transfer to the mixer fitted with the whisk attachment and whisk on medium-high speed until shiny, stiff peaks form. The bowl should no longer feel warm. Whisk in the vanilla and vinegar.
Preheat the broiler.
Place 12 ramekins on a half-sheet pan. Crumble one cookie into the bottom of each. Divide the pudding among the ramekins, then top with the meringue. Broil until golden brown. Stick 2 shortbreads into each ramekin and serve immediately.
This recipe is just fantastic with shortbreads but you can also go with an original classic using nilla cookies. That will give you an old fashioned taste.