Using an electric mixer or whisk, beat 3/4 cup heavy cream and powdered sugar until medium-stiff peaks form. Cover and chill.
Stir sugar, 1 tablespoon whiskey, corn syrup, and 1 tablespoon water in a medium deep saucepan over medium-low heat until sugar dissolves.
Increase heat, bring to a boil without stirring, and cook, occasionally swirling pan and brushing down sides with a wet pastry brush, until sugar is deep amber in color, 6–8 minutes. Remove caramel from heat; whisk in remaining 1/4 cup cream, butter, and salt (mixture will bubble vigorously).
Let cool for 5 minutes; whisk in the remaining 1/2 Tbsp. whiskey and vanilla.
Let the whiskey caramel cool slightly.
Spread 1/4 cup vanilla pudding evenly over bottom of graham cracker crust. Slice bananas into 1/4"-thick rounds. Layer half of the bananas over the pudding. Top with 1 cup of pudding. Arrange remaining bananas on the next layer and top them with the remaining pudding. Garnish with whipped cream and drizzle with whiskey caramel. Serve immediately or chill until ready to serve.