Preheat the oven to 350°F. Line a 9x9-inch square pan with parchment, leaving an overhang to lift the finished bars out, and lightly grease the parchment.
Make the shortbread by beating the softened butter and granulated sugar together in a stand mixer fitted with the paddle (or with a hand mixer) until pale and fluffy, about 2–3 minutes. Add the salt and all-purpose flour and mix on low just until the dough comes together into coarse crumbs. Press the mixture evenly and firmly into the prepared pan using the back of a spoon or a piece of parchment.
Chill the pressed shortbread in the refrigerator for 15 minutes to help it keep its shape, then bake in the preheated oven for 25–30 minutes or until the edges are lightly golden. Remove from the oven and set the pan on a wire rack to cool completely while you prepare the caramel.
For the caramel, combine the sweetened condensed milk, brown sugar, corn syrup and butter in a medium heavy-bottomed saucepan. Warm over medium heat, whisking until smooth and melted. Fit a candy thermometer to the pot and keep the mixture at a lively simmer, stirring constantly, until it thickens and reaches about 230°F (this usually takes 6–8 minutes once it starts simmering).
Remove the caramel from the heat and stir in the salt and vanilla. Pour the hot caramel evenly over the cooled shortbread, smoothing the top with an offset spatula. Allow the pan to come to room temperature, then refrigerate 25–35 minutes so the caramel firms but is still slightly tacky.
Make the chocolate layer: place the chocolate chips in a heatproof bowl. Heat the heavy cream just to a simmer (do not boil), pour it over the chocolate, and let sit for 1 minute. Stir gently from the center until the chocolate is fully melted and the ganache is glossy. If needed, microwave in 10-second bursts to smooth.
Pour the ganache over the chilled caramel and spread into an even layer. Return the pan to the refrigerator and chill at least 2 hours, or until the chocolate is fully set.
When the bars are firm, sprinkle the surface with the flaky sea salt. Lift the block from the pan using the parchment overhang and slice into 20 bars. For cleaner cuts, wipe a sharp knife between cuts or dip it in hot water and dry before slicing.