Place the cubed unsalted butter in a medium saucepan and melt over medium-low heat.
Add the packed brown sugar and milk, increase heat to medium, and stir constantly until the mixture comes to a full boil (large bubbles across the surface).
Once boiling, continue to boil and stir for 2 minutes to thicken the caramel.
Remove the pan from the heat and stir in the vanilla extract and the 1/4 teaspoon salt; taste and add more salt if desired.
Pour the hot caramel into a jar or heatproof container and let cool slightly before using, then cover.
If the caramel separates as it cools, stir or shake to recombine; if it becomes too thick after chilling, warm briefly and stir to loosen.