Combine the sugar, corn syrup, butter, and 3/4 cup of the cream in a heavy-bottomed saucepan. Bring to a boil, stirring, over medium heat. Turn the heat to medium-low. Place a candy thermometer in the pan. Boil the sugar, without stirring, until the mixture reaches 234 degrees F., (the soft ball stage).
Remove pan from the heat, and carefully add the remaining cream and vanilla. Cool slightly. Serve the sauce warm.
To store the butterscotch sauce, pour it into a heatproof jar. Cover with the lid and refrigerate for up to 2 week. To serve, loosen the cover on the jar and set jar in small pot of simmering water until heated through. Serve.
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