In a small pot combine cream, butter, vanilla and salt. Bring just to a boil and set aside.
Pour the sugar into a heavy bottomed pot with high sides. Shake to distribute sugar in an even layer over the bottom. Pour the water around the edges and stir to hydrate the sugar. Stir carefully so that no sugar gets on the sides of the pot. If you did get sugar on the sides, don’t worry. Dip a clean pastry brush (or folded paper towel) in water and wash the sugar off. Don’t be concerned with the amount of water because it will all evaporate anyways.
Pour the corn syrup into the sugar water mixture and turn on the burner to medium high. Allow the sugar to come to a boil before you disturb it. Gently swirl the pot but do not stir! This will allow you to redistribute the caramel around the pot and control the hot spots.
Continue to cook and occasionally swirl until a dark amber color is achieved.
If you have a hard time telling the color of the caramel, tilt the pot towards you so that there is only a thin layer. I find it easier to see that way. A medium amber is a perfectly acceptable color but I like to take mine to dark amber which is right when it starts to smoke but before it smells burnt.
Remove from the heat and place on a trivet. Slowly pour in your cream/butter mixture while constantly whisking. You don’t want to add the cream too fast or it will bubble up aggressively and could burn you. Don’t fear, just keep whisking. Once all the liquid is incorporated, pour into a heat safe bowl (glass, ceramic, pyrex, metal are all fine). Allow to cool to room temperature then pour into the storage container of your choice.