In a medium saucepan over medium heat, add the cubed unsalted butter. Allow it to melt completely, stirring occasionally to ensure it doesn’t brown.
Once the butter is melted, add the packed brown sugar. Stir continuously until the sugar is fully incorporated and the mixture starts to bubble.
Carefully add the milk to the saucepan. Be cautious as the mixture may bubble up. Stir until everything is well blended and smooth.
Remove the saucepan from the heat and stir in the vanilla extract and a pinch of kosher or sea salt. Taste and adjust the salt level to your preference.
Pour the warm salted caramel into a heatproof container and let it cool. It will thicken as it cools. Once cooled, store it in the refrigerator for up to two weeks.