Make shortbread crust by preheating oven to 375F degrees. Butter shallow 9x9.5 inch square baking pan. Line bottom and 2 sides with parchment paper, leaving overhang. Butter parchment. Blend together butter, brown sugar, vanilla and salt in bowl with fork. Sift in flour and blend with fork until soft dough forms. Spread dough evenly in baking pan using spatula, then prick all over with fork. Bake until golden, 15 to 20 minutes, then cool completely in pan (about 30 minutes).
To make chocolate dulce de leche, bring cream and dulce de leche to a simmer in small heavy saucepan, stirring with wooden spoon until dissolved. Whisk together yolks in bowl, then slowly whisk in hot cream mixture. Return to pan and cook over medium heart, stirring constantly, until thermometer registers 170F degrees.
Remove from heat and whisk in chocolate until melted. Pour chocolate mixture over cooled shortbread and chill, uncovered, until set (about 2 hours). Run a small knife around edges to loosen, then transfer to cutting board. Cut with hot clean knife into bars. Chill until ready to serve.