In a heavy-bottomed medium saucepan, combine the sugar, water, and corn syrup. Stir to combine carefully so it doesn't splash up the sides of the pan.
Bring the mixture to a simmer over medium heat. During this step, use a pastry brush dipped in water to brush any sugar crystals off the side of the pan, if needed.
Increase the heat to just above medium and boil for 7 to 8 minutes until the mixture turns a dark golden amber color. The color of the mixture matters more than the exact time. It can go from golden to burned quickly, so keep a close eye on it. A candy thermometer will register anywhere from 350 to 370 degrees F.
Immediately remove the pan from the heat. Add the cream, butter, vanilla and salt (do so carefully as the mixture will bubble and steam).
Stir slowly until the ingredients are well combined and the sauce is smooth. If you feel any hard sugar crystals on the bottom or sides of the pan, don't aggressively scrape them up - just leave them be and stir around them.
Pour the sauce into a jar or other container. Let cool until room temperature. Refrigerate for up to several weeks and reheat on low heat to warm for serving, if desired.
Notes
Double Batch:This sauce can easily be doubled. Use a larger pan and keep an eye on the timing; it will take a few minutes longer for the sugar/water mixture to get to the golden brown stage. How to Store Caramel Sauce:After the sauce has been made, immediately pour it into a container (so it doesn't continue to cook in the hot pan). Let it cool completely before refrigerating. This helps prevent separation or grainy texture. Rewarm lightly in the microwave for a few seconds at a time before using.