Melt the butter over medium heat in a medium saucepan.
Add the brown sugar, heavy cream, and salt to the melted butter and stir to combine. Cook for 5 minutes, stirring often.
Remove from heat and transfer to a mason jar for storing. Let cool with the lid off. Cover and refrigerate for up to 3 weeks.
Notes
To soften the caramel sauce after it's been refrigerated, microwave it for 10 seconds at a time (stirring after each heating) until it reaches the consistency you like.
To freeze: Cool the caramel sauce completely in a freezer-safe container (not glass!). Freeze for up to 3 months. The sauce can be thawed in the fridge overnight or left on the counter for a few hours and then warmed in the microwave if you like.