Sprinkle part of the sugar into a heavy sauce pan set over medium-low heat, and watch careful until it begins melting. Swirl and/or shake the pan gently every 20 seconds or so, and sprinkle more of the sugar on top of the melted parts until all the sugar is in the pan. The sugar will melt unevenly, so keep giving it a swirly shake every 20 seconds. Be patient and keep an eye on it to make sure it does not burn.
Once melted, remove from heat immediately and stir in the butter. The mixture will bubble aggressively.
Keep stirring as you add heavy cream, vanilla, and sea salt. Stir vigorously until everything is combined. Taste a spoonful of cooled caramel. If desired add another ¼ teaspoon sea salt to taste!
Pour into a pint-size jar, and allow to cool completely before using.
Notes
Store tightly covered in fridge for up to 1 month.