Pre-heat the oven to 350 degrees Fahrenheit. Prepare a 9-by-9-inch pan by lining the bottom with a long strip of parchment paper, making sure that the paper is long enough so the ends hang over the sides of the pan. Spray the parchment and pan with nonstick cooking spray.
In a large bowl, stir together the sugar, salt, and melted butter with a fork. Add the egg yolk and mix well.
Finally, add the flour and stir until the crust is moist clumps. Transfer the dough into the parchment lined pan and press down with your hands or the bottom of a measuring cup to make an even layer. Refrigerate the crust for 15-20 minutes, until chilled.
Bake the crust for about 25 minutes, until lightly golden brown on top. Let the crust cool completely while you prepare the caramel topping.
To make the caramel topping, combine the butter, brown sugar, corn syrup, salt, granulated sugar and cream in a medium heavy-bottomed saucepan. The caramel will bubble up as it cooks, so be sure to use a pan where the mixture can triple in size.
Bring the mixture to a boil, stirring occasionally, and make sure that all of the sugar is dissolved. Once it's boiling, insert a candy thermometer and cook, stirring occasionally, until it reads 250 degrees F. (This will produce a bar with a medium-firm chew. For a softer chew, cook to 245 F, and for a really firm chew, shoot for 255 F.)
Once at the right temperature, remove the pan from the heat, stir in the vanilla extract, and pour the caramel on top of the shortbread.
Let the caramel sit until firm: about 2-3 hours at room temperature. You can speed up the process by refrigerating it, but it will get very hard in the refrigerator, and you might need to let it come back to room temperature before cutting and serving.
Once the caramel has set, remove the bars from the pan and cut it into small square or rectangles. Finish with a little pinch of flaked sea salt, and enjoy! These bars are best served and eaten at room temperature. If you have cooked them a little too long and they're harder than you like, microwave them for 5-8 seconds and the caramel will soften to a wonderfully chewy texture.