In a small saucepan over medium-low heat, melt the butter. Once the butter is completely melted, stir in the brown sugar. Whisk the mixture briskly and constantly for 2 minutes on medium-low heat.
The mixture will barely start to bubble. Briskly stir in the heavy whipping cream.
Add in the vanilla extract. Raise the heat to medium, and briskly stir for another 2 minutes.
Remove the mixture from the heat. It will be relatively thick, but not as thick as a caramel sauce. Pour the mixture into a heat-safe jar, and place it in the fridge.
After about 30 to 45 minutes, the mixture will be a thick and delicious caramel sauce. Now it's time to stir in a little bit of salt to your desired preference. Start with 1/2 teaspoon, and increase the amount of salt to desired preference.