In a medium saucepan, combine the sugar and water over medium-high heat. Stir. Bring the mixture to a boil and shake/swirl the pan very often (don't stir it while it's boiling) until it turns a medium amber color (should take 12 to 15 minutes). If sugar crystals gather along the sides of the pan during the cooking process, you can use a pastry brush dipped in water to brush the sugar down the sides of the pan so that it becomes incorporated into the boiling mixture.
Remove the pan from heat and pour in the cream. It will bubble up like crazy. Give it a whisk, then add in the butter, vanilla and sea salt. Whisk again until everything is nice and smooth. It should be the color of caramel. Cool it in the pan, or pour it into a large measuring cup so that it will be easier to transfer to jars when cooled.
Divide the sauce evenly among the four jars. Place lids and labels on and refrigerate until ready to use or gift to friends. The sauce must be kept refrigerated and it will stay fresh for 2 to 3 weeks.
Notes
*I like to boil my jelly jars and lids for a couple of minutes to really get rid of any grime that might be in there from packaging. Then I just let them dry thoroughly before adding the sauce.
*If your sauce solidifies (I speak from experience), you either let it cook too long or the heat wasn't high enough. Pull it off the heat when it is a nice, medium amber color. It's important that it maintains a nice boil at medium-high heat and that you don't take yours eyes off of it. Keep swirling the pan and don't let it burn!
*Serving suggestions: Serve with apples, cheesecake, ice cream, or incorporate it into a milkshake!