Spray bottom and sides of a 9 by 11-inch baking pan with vegetable oil or rub with 1 tablespoon butter. In a small heavy saucepan, combine cream, evaporated milk, and sweetened condensed milk. Set aside to warm later.
In a large, heavy saucepan, combine corn syrup, sugar, water, and salt. Over high heat, cook until sugar is dissolved, about 6 to 8 minutes, brushing down sides of pan with a pastry brush dipped in water to remove any sugar crystals. Stop stirring, insert candy thermometer, reduce heat to medium and let come to a boil. Cook, without stirring, until temperature reaches 250 degrees F (hard-ball stage), about 45 to 60 minutes.
Meanwhile, place cream and milk mixture over low heat and stir until warm. Do not boil.
When sugar reaches 250 degrees F, stir in the warm cream and the pieces of butter. Stirring constantly, cook over medium heat until thermometer reaches 244 degrees (firm ball stage), 45 to 60 minutes. Stir in vanilla. Immediately pour into prepared pan without scraping pot. Let stand, uncovered, at room temperature for 12 to 24 hours without moving. This is the most difficult part, as you will want to eat it!
To cut into candies, coat a cutting board or marble slab generously with vegetable oil spray. Unmold caramel by turning upside down onto oiled surface. Cut into 1-inch by 1 1/2-inch pieces with a very sharp, heavy knife. Wrap with precut waxed paper squares, twisting ends to seal. If you don't wrap them, the caramel pieces will stick together.
Options: Add nuts to bottom of pan and pour caramel over nuts. Cut as above. Or, pour caramel onto pieces of cut up fruit such as apples or pears.