For the shortbread layer: Preheat the oven to 350 degrees F. Using a pastry brush, butter a 9-by-13-inch baking dish and coat with flour, tapping off excess.
Put the flour, sugar and salt in a food processor and pulse. Add the butter and pulse until the dough just comes together. Press the shortbread mixture into the prepared pan and bake until golden brown around the edges, about 20 minutes. Remove from the oven and let cool completely.
For the cookie butter layer: In a 5-quart saucepan over moderately-low heat, combine the sweetened condensed milk, brown sugar, cookie butter and salt. Slowly bring the mixture to a boil, stirring continuously. Continue stirring over the heat until the mixture becomes thick and amber in color, about 15 minutes. Pour the mixture over the cooked shortbread and spread evenly using an offset spatula. Cool to room temperature.
For the chocolate topping: In a bowl set over a saucepan of simmering water, melt the chocolate with the oil. Once the chocolate has melted, pour it over the cooled caramel layer. Cool at room temperature for about 10 minutes, and then put in the refrigerator to cool completely, allowing the chocolate to slightly harden but not too hard. Cut into 2-inch pieces. Garnish with flaky salt before serving.