In a medium, heavy bottomed saucepan, bring sugar, evaporated milk and heavy cream to a boil over medium heat. Add corn syrup and continue cooking until mixture reaches 230 degrees on a candy thermometer.
Add butter, vanilla; cook, stirring constantly, until caramel reaches 240 degrees. Remove from heat, stir in salt; pour into a lightly oiled 13x9-inch baking dish (parchment paper in pan helps).
Let cool at least 1 hour. Invert onto a cutting board covered with waxed or parchment paper and cut into 1-inch pieces with a sharp, lightly oiled knife. Caramels can be wrapped in waxed or parchment paper or cellophane. (To serve candy-store style, wrap individual pieces in parchment paper and secure ends with a twist.) Store airtight at cool room temperature (around 65) or in the refrigerator; will keep up to 3 weeks.