Beat butter in a medium bowl with an electric mixer until creamy. Beat in powdered sugar and 1 teaspoon vanilla extract. Combine flour and salt in a medium bowl; gradually beat into butter mixture.
Press dough into a greased, aluminum foil-lined 9- x 9-inch baking pan. Bake at 350° for 23 to 25 minutes. Set aside.
Combine sugar, 1/2 cup heavy cream, corn syrup, and butter in a 2-quart heavy pot. Cook over medium-low heat, stirring often, until butter melts and sugar dissolves. Increase heat to medium, and bring to a boil. Boil, without stirring, until mixture reaches 238° (just past soft ball stage) on a candy thermometer.
Combine remaining 1/2 cup cream and remaining 1 teaspoon vanilla extract; carefully pour into sugar mixture. (Mixture will bubble.) Boil until mixture returns to 238°. Pour over shortbread crust. Let stand at room temperature or refrigerate until caramel is firm.
Pour Chocolate Ganache over caramel, smoothing with an offset spatula. Sprinkle with sea salt. Let stand in a cool place until chocolate is firm. Cut into bars.