In a saucepan over medium heat, add sugar, water, and salt. Whisk frequently until the mixture comes to a low boil and sugar is dissolved (8-10 minutes).
Reduce heat to medium-low, cover, and simmer for 10 minutes.
Add chopped banana pieces, simmer for 10 more minutes.
Strain out bananas and set the syrup aside. You will use this in both the pie and the pie crust.
In a large bowl, combine the sugar, cornstarch, and salt.
Add the eggs, whisking to combine.
Add the milk and simple syrup and whisk until well combined, about 30 seconds.
Pour the mixture into the saucepan and cook over medium-low heat, stirring constantly until thickened, approximately 5 to 10 minutes.
Remove from the heat and whisk in the butter, 1 cube at a time.
Whisk in the vanilla extract.
Cover with plastic wrap and chill 2 hours.
In a food processor, add cookies and process until you have a fine crumb.
Pour in melted butter and simple syrup and pulse until the mixture is combined.
Press in the bottom and up the sides of a 9-inch pie pan. Chill for 30 minutes.
Add heavy cream to mixing bowl, mix starting with low speed, then gradually increase to medium speed until the cream starts getting thicker (the gradual speed progression prevents you from spraying yourself with cream).
When the cream starts to thicken stop the mixer, add in the powdered sugar and then resume mixing again starting with low speed and increase to medium speed up to high speed.
The cream will thicken and start to peak. Mix on high speed until the cream is thick and stiff.