Preheat oven to 350F. Line a loaf pan with parchment paper.
To make the crumb, cream the butter by itself for a min with a paddle hook, then add the sugar, mixing to incorporate. Add the flour, and combine until crumbs form. Add milk and mix to incorporate.
Spread the dough in the loaf pan, bake for 20min. Let cool.
While crust is cooling, prepare the caramel. Melt butter and sugar, then add corn syrup and sweetened condensed milk. Bring to a rapid boil over medium-high heat, decrease to medium heat (should still be bubbling), and continue cooking until the mixture achieves deep caramel color. Can take 5-10 minute. Keep whisking all the way!
Add sea salt, and pour the caramel over the shortbread. Sprinkle pretty salt as desired. Keep in the fridge until all set (1-2hr).