Melt the butter in a tall heavy saucepan.  Make sure that your saucepan is tall because the mixture will more than double in volume as it cooks.

Add the brown sugar, cream, corn syrup, and vanilla.  If making this for grown-ups, you could omit the vanilla and stir in a tablespoon of your favorite hard drink.  Using Bourbon or Whiskey works very well. 

Cook at low to medium heat, stirring occasionally with a wooden spoon until the sugar dissolves and the sauce simmers and thickens.  Continue to stir occasionally throughout the process.