In a small saucepan, combine the brown sugar, salt, and a splash of water over medium heat. Stir gently to ensure that the sugar is evenly moistened and begins to dissolve.

Continue to cook the bubbling mixture, allowing it to turn a deep amber color. Monitor closely to prevent burning.

Carefully add the unsalted butter into the hot caramel mixture, stirring continuously until fully melted and blended.

Gradually pour in the whole milk, stirring constantly, and place the saucepan back over medium-low heat until warmed through, about 3-4 minutes.

Once heated, remove from heat and stir in the vanilla extract. Froth some milk separately if desired.

Pour into mugs and enjoy immediately, garnishing with whipped cream, frothed milk, or a sprinkle of cinnamon if desired.