In a medium-sized saucepan, combine the granulated sugar, water, and corn syrup. Stir with a wooden spoon until the sugar is nearly dissolved.
Turn the heat to medium and bring to a simmer. From this point on, do not stir the caramel.
Periodically brush the interior walls of the saucepan with a wet pastry brush to wash away any stray sugar crystals and prevent graininess.
Watch closely as the syrup bubbles, turns clear, and eventually transitions into a deep amber (the color of a copper penny).
Remove from heat immediately and carefully whisk in the room-temperature unsalted butter until melted.
Slowly pour in the room-temperature heavy cream, vanilla extract, and kosher salt while whisking continuously.
Return the saucepan to medium heat and cook, stirring constantly, for 2 minutes. Remove from heat and let cool completely to room temperature so it thickens into a silky smooth sauce.
Notes
Ensure the heavy cream and butter are at room temperature to avoid splattering, seizing, and separation.
Never stir the caramel while it is boiling to prevent sugar crystallization.
Use a pastry brush dipped in water to wipe down the sides of the pan during cooking.
The sauce will look quite runny when first finished, but it will thicken significantly as it cools down to room temperature.
Store in an airtight glass jar in the refrigerator for up to 2 weeks, and microwave for 20 to 30 seconds before using.
Freeze in a freezer-safe container for up to 3 months, and thaw overnight in the refrigerator before reheating.