In a medium, heavy-bottom saucepan, combine sugar, evaporated milk, and heavy cream. Bring to a boil over medium heat. Add the corn syrup and continue cooking until the mixture registers 230 degrees F on a candy thermometer, about 10 minutes.
Stir in the butter and vanilla and continue cooking, stirring constantly, until caramel reaches 240 degrees F. Remove from heat and stir in salt; carefully pour into a lightly oiled, parchment-lined 9 by 13-inch baking dish.
Let the caramels cool at least 1 hour. Invert the caramels onto a cutting board covered with waxed or parchment paper. Cut into 1-inch pieces with a sharp, lightly oiled knife. Caramels can be wrapped in waxed or parchment paper. Store them at room temperature in an airtight container or in the refrigerator up to 3 weeks.
This recipe was provided by professional chefs and has been scaled down from a bulk recipe provided by a restaurant. The Food Network Kitchens chefs have not tested this recipe, in the proportions indicated, and therefore, we cannot make any representation as to the results.