Caramel Banana Pudding

Add 50 g unsalted butter to a saucepan. Cut 1 banana into pieces and cook it in the butter for 1 minute until soft. Add 90 g granulated sugar, 500 ml milk, and ¼ tsp salt, then gently heat the mixture without boiling.
Separate 3 egg yolks and whisk them in a bowl. Add 30 g cornstarch and whisk until smooth. Blend the warm banana mixture until smooth, pour it over the egg yolk mixture, and whisk in 1 tsp vanilla extract. Return everything to the saucepan and cook over low-medium heat, whisking every minute until the mixture begins to bubble, about 8 minutes, then whisk continuously until thickened. Transfer the pudding to a bowl, let it cool to lukewarm, cover with plastic wrap, and refrigerate until chilled.
Add 200 g granulated sugar and 120 ml water to a saucepan and cook over low-medium heat until melted and bubbling. Pour in 120 ml heavy cream, whisk until smooth, and transfer the caramel sauce to a bowl. Slice 3 bananas and mix them into the caramel sauce until coated.
Remove the pudding from the refrigerator and whisk until smooth. In a bowl, beat 180 ml heavy cream for about 4 minutes until slightly thickened. Assemble the dessert by adding pudding, caramel-coated bananas, and pieces of 4 cookies into serving glasses. Add another layer of pudding and caramel bananas, then top with whipped cream and garnish with 5 g dark chocolate, shaved.