Preheat the oven to 350 degrees with a rack in the center position. Line the bottom and sides of a 9- by 13- by 2-inch pan with an aluminum foil sling.
Combine the flour, confectioners' sugar, and salt in the bowl of a food processor. Pulse to combine. Add the butter and pulse until the dough just comes together, about 1 to 2 minutes.
Spread the dough into the prepared pan and press firmly to smooth the top. Dock the dough by pricking with a fork, making marks spaced about 1 inch apart.
Bake the shortbread until it is golden brown and firm to the touch, about 35 minutes. Set aside to cool completely in the pan.
Spread the dulce de leche over the dough forming an even layer using a small offset spatula. Refrigerate until slightly firm, about 1 hour.
Place 2 cups of chocolate in a heatproof bowl. Set over a pan of gently simmering water and stir with a rubber spatula until melted, about 1 to 2 minutes. Remove from heat and add the remaining ? cup chocolate. Stir with a rubber spatula until smooth. Spread the chocolate over the dulce de leche using a small offset spatula. Sprinkle with sea salt.
Let stand at room temperature until the chocolate sets, about 10 minutes. Using the aluminum foil as a sling, carefully remove the layered cookie from the pan. Peel back the aluminum foil and transfer to a cutting board.
Using a serrated knife, cut in half crosswise, then cut both pieces in half lengthwise, forming 4 quarters, each about 9- by 3-inches. Cut each quarter crosswise into 8 bars about 1- by 3-inches. Store at cool room temperature for up to 2 hours or refrigerate for up to 1 week.