Butter a 9-inch square baking dish. Butter the sides of a heavy 2-quart saucepan.
Combine sugars, cream, milk and butter in saucepan. Cook over medium heat, stirring
constantly, until sugars dissolve and mixture comes to a boil. Cook to soft-ball
stage (238 degrees F on candy thermometer), stirring only if necessary. Immediately
remove from heat and cool to lukewarm (110 degrees F). DO NOT STIR.
Add vanilla extract and beat vigorously until mixture is very thick and starts
to lose its gloss.
Quickly stir in walnuts and spread into prepared baking dish.