1. Make shortbread crust: preheat oven to 375°F with rack in middle. Butter a shallow 9- to 9 1/2-inch square baking pan (1 to 1 1/2 inches deep). Line bottom and 2 sides with parchment paper, leaving an overhang. Butter parchment.
2. Blend together butter, brown sugar, vanilla, and salt in a bowl with a fork. Sift in flour and blend with fork until a soft dough forms.
3. Spread dough evenly in baking pan using an offset spatula or back of a spoon, then prick all over with fork.
4. Bake until golden, 15 to 20 minutes, then cool completely in pan on a rack, about 30 minutes.
5. Make chocolate dulce de leche: bring cream and dulce de leche to a simmer in a small heavy saucepan, stirring with a wooden spoon until dulce de leche has dissolved.
6. Whisk together yolks in a bowl, then slowly whisk in hot cream mixture.
7. Return to pan and cook over medium heat, stirring constantly, until pan is visible in tracks of spoon and mixture registers 170°F on an instant-read thermometer. Remove from heat and whisk in chocolate until melted.
8. Make bars: pour chocolate mixture over cooled shortbread and chill, uncovered, until cold and set, about 2 hours.
9. Run a small knife around edges to loosen, then transfer to a cutting board using parchment. Cut with a hot clean knife (dip in hot water and wipe clean between cuts) into 24 bars. Chill until ready to serve.

Makes 24 bars

Make Ahead: Chocolate dulce de leche bars can be chilled in an airtight container up to 1 day.