Caramel Budino with Salted Caramel Sauce

Cookie Crust

• 1 cup finely ground chocolate cookie crumbs (such as Nabisco Famous Chocolate Wafers; about 20 cookies)
• 2 tablespoons unsalted butter, melted
• 1/8 teaspoon kosher salt

Budino

• 3 cups whole milk, divided
• 1/4 cup cornstarch
• 3/4 cup (packed) dark brown sugar
• 5 large egg yolks
• 3 tablespoons unsalted butter
• 2 teaspoons dark rum
• 1 teaspoon kosher salt

Salted Caramel Sauce

• 3/4 cup plus 2 tablespoons heavy cream, divided
• 1/2 vanilla bean, split lengthwise
• 1/2 cup sugar
• 2 tablespoons light corn syrup
• 4 tablespoons (1/2 stick) chilled unsalted butter, cut into 1/2' cubes
• 1/4 teaspoon kosher salt
• Lightly sweetened whipped cream

• To assemble crust, mix cookie crumbs, butter, and salt in a medium bowl. Place 2 tablespoons in a small bowl; cover and chill for garnish. Press 2 tablespoons cookie mixture onto the bottom of each of eight 8-ounce mason jars or ramekins.

• Make budino, by whisking 1/2 cup milk and cornstarch in a small bowl; set aside. Heat remaining 2 1/2 cups milk in a small saucepan just to a simmer; set aside. To make caramel, stir sugar and 3/4 cup water in a heavy saucepan over medium heat until sugar dissolves. Increase heat; cook without stirring until an instant-read thermometer registers 210°–220°
• Line a sieve with a double layer of cheesecloth and set over a large pitcher. Whisk egg yolks in a large bowl. Gradually whisk in hot milk, then cornstarch mixture. Slowly whisk in caramel. Return mixture to saucepan. Whisk constantly over medium heat until mixture thickens and a thermometer registers 175°, about 3 minutes. Remove from heat; whisk in butter, rum, and salt. Pour through prepared sieve.
• Pour 1/2 cup budino over crust in each jar. Cover; chill until set, 4–5 hours. DO AHEAD Can be made 1 day ahead. Keep chilled.

• Begin the salted caramel sauce by placing cream in a small pitcher. Scrape in seeds from vanilla bean; add bean. Set aside.
• Stir sugar, corn syrup, and 2 tablespoons water in a heavy saucepan over medium heat until sugar dissolves. Increase heat to medium-high; boil, occasionally swirling pan and brushing down sides with a wet pastry brush, until deep amber color forms, 5–6 minutes. Remove from heat; gradually add vanilla cream (mixture will bubble vigorously). Whisk over medium heat until smooth and thick, about 2 minutes. Remove from heat; whisk in butter and salt. Strain into a heatproof bowl. Let cool slightly.
• Spoon 2 tablespoons caramel sauce over each budino. Top with whipped cream. Sprinkle some of reserved cookie crumbs over each.