Lightly grease the sides of a heavy 4-quart saucepan.
Add the sugars, salt, corn syrup, milk, evaporated milk, and cream.
Cook over low heat, stirring constantly, until the sugar is dissolved.
When the mixture comes to a boil, cook over medium heat, stirring constantly to prevent scorching, to 234°, or until a small amount of syrup dropped into cold water forms a soft ball.
Remove from the heat and cool to lukewarm (110°) without stirring.
Add the vanilla and beat until the mixture loses its gloss and is thick enough to hold a shape.
Add the nuts and quickly pour out into a lightly greased 8-inch square oan.
Cool until firm, then cut into squares.