Over medium heat, melt the butter in a medium saucepan (not nonstick).
Add the brown sugar, salt and cream.
Stir gently with a heat resistant spatula, blending well.
Bring the mixture to a boil (at this point I like to switch to using a whisk).
Keep the mixture at a consistent low boil (you should see bubbles throughout), whisking often, and cook for 4 to 4 ½ minutes.
Immediately remove the saucepan from the heat and whisk in the vanilla.
Carefully pour the mixture into the jar or container and allow to cool before covering and refrigerating.
Note that the sauce will thicken as it cools; it can be rewarmed, uncovered, in the microwave for a short 15 to 25 seconds