Butterscotch Budino with Salted Caramel Sauce

COOKIE CRUST
1c finely ground chocolate cookie crumbs (such as Nabisco Famous Chocolate Wafers, Biscoff or Swedish pepparkakor; about 20 cookies)
1/8 teaspoon kosher salt

2 T unsalted butter, melted

BUDINO

3 cups whole milk, divided

1/4 cup cornstarch

3/4 cup (packed) dark brown sugar

5 large egg yolks

3 T unsalted butter

2 t dark rum

1 t kosher salt

SALTED CARAMEL SAUCE

3/4 cup plus 2 T heavy cream, divided

1/2 vanilla bean, split lengthwise

1/2 cup sugar

2 T light corn syrup

4 T (1/2 stick) chilled unsalted butter, cut into 1/2' cubes

1/4 t kosher salt

Lightly sweetened whipped cream

Mix cookie crumbs, butter, & salt in a medium bowl. Place 2 T in a small bowl; save for garnish. Press 2 T cookie mixture onto the bottom of each of eight 8-ounce mason jars or ramekins.

BUDINO

Whisk 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 I/2 cup budino over crust in each jar. Cover; chill until set, 4-5 hours. DO AHEAD Can be made I day ahead. Keep chilled.

SALTED CARAMEL SAUCE

Place 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 T caramel sauce over each budino. Top with whipped cream. Sprinkle some of reserved cookie crumbs over each.