Melt butter in a small saucepan over medium-high. Add brown sugar and salt, and cook, whisking constantly, until sugar dissolves and mixture is bubbly, about 5 minutes. Add half-and-half, and whisk until mixture comes back to a boil, about 1 more minute. Remove from heat, and cool 5 minutes. Stir in vanilla. Serve warm or at room temperature.
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