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 â…“ 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.
#### Salted Caramel
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.
#### Brown Butter Wafers
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.
#### Whipped Cream
Just before assembling, whip heavy cream, sugar, and vanilla until soft peaks form.
### Assembly
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.