Line an 8×8″ pan with parchment paper, leaving some hanging over the sides to make removal easier.
In a large bowl, combine the butter, sugar, and salt with a pastry cutter or fork. Add the egg yolk and continue mixing.
Add the flour and combine the dough until coarse crumbs form. Transfer the dough into the prepared pan and press it down into one even layer. Refrigerate for 30 minutes.
Bake for 25 minutes, until slightly golden brown. Set aside to cool.
For the caramel, combine the butter, brown sugar, corn syrup, salt, sugar, and heavy cream. Bring to a boil and stir for about 5-10 minutes until caramel reaches the “soft ball stage” and using a candy thermometer make sure it reaches 230°.
Remove from heat, stir in the vanilla and pour caramel over the shortbread.
Refrigerate for at least 3 hours, then sprinkle with sea salt. I like to use the parchment paper "handles" over hanging to lift out of the pan and cut into finger length cookies or squares. Store caramel shortbread in the fridge until you’re ready to eat them.