Melt the butter, in a heavy saucepan.
Add the brown sugar, salt, and heavy cream, and heat to boiling over medium-high heat, stirring constantly.
Boil gently over medium-low heat, stirring occasionally, until mixture is no longer grainy, about 2 to 3 minutes.
Immediately remove from heat and stir in vanilla and mix until smooth and well combined.
Serve immediately or store in a jar with a tight-fitting lid. Store in refrigerator until ready to use.
When ready to use, remove lid and microwave for 30 seconds at a time and stir. Continue heating until smooth and pourable.