Melt butter with brown sugar: In a medium saucepan, melt the 4 Tablespoons butter over medium heat. Stir in the 1/2 cup brown sugar, 1/2 cup heavy cream and 1/4 teaspoon salt. Bring to a light boil, stirring occasionally. This will take about 3 minutes.
Cook the sauce: Reduce the heat to medium-low and allow it to come to a boil, stirring frequently. Be careful no to let it burn. This will take about 5 minutes. If you would like to use a candy thermometer, cook it until it reaches 220°F.
Stir in vanilla and cool: Remove from heat. Stir in 1 teaspoon vanilla. Cool for about 5 minutes, the transfer to a jar for serving.
Notes
Storage: Store in a covered container in the refrigerator for up to 2 weeks. Reheat in the microwave or on the stove.