1c finely ground chocolate cookie crumbs (such as Nabisco Famous Chocolate Wafers, Biscoff or Swedish pepparkakor; about 20 cookies)
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 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.
