Pour the sugar into a 12-inch skillet and shake the pan to evenly disperse it.
Set the pan over medium heat and cook, without stirring or swirling the pan, until it begins to melt around the edges and bubbles begin to pop up in the surface of the sugar, 3 to 4 minutes.
Using a heat-proof silicone spatula, gently stir the sugar, pulling it into the center of the pan, until it is liquified.
Continue stirring and cook until the sugar turns deep golden brown, 2 to 3 minutes.
Remove the pan from the heat and pour in the cream; (it will bubble up and the sugar will seize.)
When the bubbling subsides, return the pan to medium heat and stir constantly the sugar has completely dissolved and the sauce is smooth.
Stir in the butter and vanilla until combined.
Cool to room temperature before transferring to an airtight container and storing in the refrigerator for up to 5 days.
Rewarm the sauce gently until slightly thinner before using.