Melt butter over medium heat in a saucepan. Add in the brown sugar once the butter has melted and stir / whisk until all the sugar is wet.
Let the butter-sugar mixture cook over medium heat, stirring occasionally for 3 minutes. The mixture will become more liquid and less grainy.
Lower the heat to low and whisk in the cream. When the cream has been incorporated, turn the heat back up to medium and let the mixture cook for another 2 minutes, whisking frequently.
Remove the pot from the heat and stir in the vanilla extract. Taste the butterscotch sauce (be careful it's hot!) and whisk in the salt, a little bit at a time, tasting after each addition until you like how it taste.
Serve it warm or at room temperature.
To keep: let the sauce cool to room temperature. Transfer the sauce to a glass jar with a tight fitting lid. Store it in a refrigerator for up to 1 month. Reheat in a microwave or in a saucepan.