In a medium saucepan, add sugar and water. Stir on medium high heat until dissolved, then let simmer for 8-10 minutes, stirring frequently with a wooden spoon or metal whisk. Half way through cooking the sugar will completely clump up and look like a salt block, don't worry. Let it cook a little longer (continue stirring) and it will start to brown and turn into an amber liquid again. At this point keep a close eye on the sugar because you don't want it to burn.
Once your sugar has become a nice amber liquid, add the butter and stir constantly. Be careful because anything you add to the sugar will cause it to bubble rapidly, creating steam. Keep face and hands clear of the saucepan opening but continue to stir constantly.
Once butter is completely melted and incorporated into sugar mixture, slowly pour half & half into saucepan, stirring constantly. Add vanilla extract and let simmer for about 60 seconds.
Remove sauce from heat and add salt, mixing it in well. Let cool for 10-15 minutes prior to using as it will thicken as it cools down. Enjoy!
Notes
When you add the butter, if you keep it on too long it may start to separate in the sugar mixture. Don't worry! Simply remove the sauce from the heat and stir quickly to combine. Return to heat and move on to the next step.This sauce holds up very well in the refrigerator. To use simply reheat in the microwave until desired consistency.