1) Line an 8-by-8-by-2-inch pan with foil.
2) Lightly butter foil.
3) In a heavy, 3-1/2-quart saucepan, combine sugar, corn syrup, cream, and butter.
4) Over medium heat, cook, stirring with wooden spoon, until sugar is dissolved.
5) Continue cooking, stirring occasionally, to 245 F on candy thermometer, or until a little in cold water forms a firm ball.
6) Remove the saucepan from heat.
7) Add vanilla and walnuts.
8) In the prepared pan, turn out the mixture and let cool for 1 hour.
9) Serve the walnut caramels as sweet dish.