Heat the cream in the microwave or on the stove top until warm but not boiling. Set aside.
In a pot or saute pan with a large surface area, spread sugar in a thin, even layer. Turn burner to medium and heat until parts of the sugar begin to liquefy. The sugar will form clumps before going liquid. This part feels like it takes awhile, but once it starts to melt it will go fast.
Gently stir, making sure unmelted sugar comes in contact with the greatest heat source. Continue, stirring often, until all the sugar is melted and turns a deep amber color. If it seems to be going too fast, lower the heat.
Dribble a small stream of the cream into the caramel whisking constantly. It will bubble a lot and be slightly terrifying. Continue to add the cream, a little at a time, whisking. Once about half the cream is incorporated, you can add the rest in a steady stream, continuing to whisk until smooth.
Stir in vanilla and salt, to taste. Serve warm or pour into an airtight container and cool completely, then refrigerate. The caramel will thicken considerably when cold. It's great used as a dip this way, or you can rewarm it in the microwave to drizzle on your favorite drinks and desserts.