Banana Bread Bombe

Name: Banana Bread Bombe
Ingredients: Nonstick cooking spray, for greasing the pan; 1 cup sugar; 1 stick (8 tablespoons) unsalted butter, at room temperature; 2 large eggs; 3 ripe bananas (about 1 pound); 2 cups all-purpose flour (see Cook's Note); 1 teaspoon baking powder; 1 teaspoon baking soda; 1 teaspoon ground cinnamon; 1 teaspoon kosher salt; 1 cup plus 1 tablespoon whole milk; Two 3.4-ounce boxes instant banana pudding mix; 4 cups heavy cream; One 15-ounce box vanilla wafer cookies (about 95 cookies); Warm caramel sauce, for drizzling