How to Make It
Combine 1 cup cream and miso in a small saucepan. Bring just to a simmer over medium, and remove from heat. Combine 3/4 cup granulated sugar, 2 tablespoons water, and corn syrup in a medium saucepan. Cook over medium-high, without stirring, until a deep-amber caramel forms, 5 to 6 minutes. Remove from heat and gradually whisk in warm cream mixture (mixture will bubble up). Let cool 10 minutes. Pour through a fine wire-mesh strainer into a heatproof container; discard solids.
Whisk together 1/2 cup milk, 1/2 cup granulated sugar, cornstarch, and egg yolks in a medium bowl. Combine remaining 3 cups milk and remaining 1/2 cup granulated sugar in a medium saucepan. Bring to a simmer over medium. Remove from heat and very gradually whisk hot milk mixture into egg mixture to temper it. Return mixture to saucepan, and bring to a boil over medium-high. Cook, whisking constantly, until thickened, 1 to 2 minutes. Remove from heat, and whisk in 6 tablespoons butter, 1 tablespoon at a time, until incorporated. Whisk in vanilla and 1 teaspoon salt. Transfer pudding to a medium bowl and press a piece of plastic wrap directly on surface. Let cool completely, and refrigerate until well chilled, about 4 hours. Fold in bananas and refrigerate 30 minutes.
Preheat oven to 325°F and line a large rimmed baking sheet with parchment paper. Melt 1/4 cup butter and kokuto in a small saucepan over medium, stirring, until sugar is dissolved, about 2 minutes. Whisk together graham cracker crumbs, flour, light brown sugar, and 1/2 teaspoon salt in a medium bowl. Stir in butter mixture until crumbs are evenly moistened. Spread mixture in a 1/4-inch-thick layer on prepared baking sheet. Bake in preheated oven until dry and crisp, about 16 minutes, breaking up and stirring crumbs halfway through baking. Let cool completely. Crush into fine crumbs.
Place 1 cup cream in a medium bowl. Beat with a hand mixer on medium-high speed until stiff peaks form, about 3 minutes.
Spoon banana pudding into 8 (8-ounce) glasses. Top evenly with caramel, whipped cream, and crumb topping. Serve immediately.
Kokuto (Japanese brown sugar) can be purchased online at chefshop.com or substituted with dark brown sugar.