Prepare a bowl with a fine mesh sieve on top.

In a separate bowl, whisk together cornstarch and sugar. Add eggs and whisk until smooth. Set aside.

In a saucepan, heat milk, vanilla bean paste, and salt over medium-high heat until just under a boil, stirring occasionally.

Gradually add ⅓ of the hot milk to the egg mixture, whisking constantly. Pour the egg-milk mixture back into the remaining milk. Whisk over medium heat until thickened, resembling lightly whipped cream. Remove from heat immediately and strain through the sieve into a bowl.

Cool for 10 minutes, stirring occasionally. Mix in butter one piece at a time until smooth. Cover with plastic wrap, pressing it directly onto the surface. Refrigerate for 30 minutes to 1 hour.

In a medium pot, combine sugar, water, and corn syrup. Boil over medium heat until amber-colored, about 8 minutes. Meanwhile, heat heavy cream and vanilla bean paste in a small pot until just under a boil. Set aside.

Slowly pour warmed cream into the amber sugar syrup, whisking until smooth. Cool for 5 minutes.

Add butter one tablespoon at a time, then add sea salt. Whisk until smooth. Set aside.

Break wafers into halves.

In a heavy saucepan over medium heat, brown the butter until nutty smelling and brown bits form. Stir in wafers. Set aside.

Just before assembling, whip heavy cream, sugar, and vanilla until soft peaks form.

Fold together pastry cream and half the whipped cream. Reserve the other half for serving.

Slice bananas into ¼ inch slices.

Layer the pudding: a third of the pastry cream, a drizzle of caramel, half the bananas, half the wafers. Repeat for a second layer. Top with the remaining pastry cream and whipped cream.

Refrigerate for 1-4 hours before serving. Best served the same day.