Using an electric hand or stand mixer, cream butter and sugar in a large bowl on low speed until combined, then increase to high speed and beat for 2 minutes.
Scrape the sides then add the vanilla, flour, and salt. Mix on low speed until the dough you do not see any flour streaks. Do not overmix.
Refrigerate for 30 minutes.
When ready to bake, preheat the oven to 375°F. Portion into 2 tablespoon balls, then press the center of the cookie with a cookie scoop or spoon. Gently pinch the dough with your fingers to seal any cracks.
Bake 7-10 minutes, or until the edges are just starting to brown. Remove from the oven and gently press once more with a cookie scoop.
Cool for 3 minutes on the baking sheet, then transfer to a cooling rack and completely.
Add brown sugar, butter, and cream to a small saucepan and bring to a boil over medium heat. Once boiling, set a timer for 60 seconds. Once the timer has gone off, turn off the burner and remove the pan.
Stir in the vanilla.
Remove from heat and spoon into cookies, without overfilling.
Sprinkle with sea salt while still hot, before caramel sets.
Let caramel set and firm.
Enjoy!