In a medium to large saucepan, add sugar, water and corn syrup. Bring to a boil over high heat, whisking until sugar is dissolved.
Boil mixture for 5 to 12 minutes, until it turns caramel-colored. Only stir if necessary during this step. Watch very closely after the first 5 minutes and do not let it burn – the mixture will change from pale amber to caramel color very quickly. When it does, reduce heat to low.
Very slowly and carefully add cream, stirring gently. The mixture may bubble up considerably, so stand back if needed. (This is why you are using a large-ish sized pan)
Add vanilla and salt, to taste.
Whisk until sauce is combined and smooth, then let boil for one minute to thicken.
Transfer sauce to a glass or other heat-safe container. Allow to cool, uncovered, to room temperature. Sauce will thicken as it cools.
Sauce will keep in an airtight container at least a month at room temperature.