1. In 4-qt. saucepan with candy thermometer attched, stir together sugar, water and light corn syrup. With pastry brush dipped in water, brush any sugar crystals off side of pan. Heat to boiling on medium-high without stirring, about 3 minutes. Boil until dark amber (320 to 345 degrees on candy thermomter), about 9 minutes.
2. Working quickly, remove pan from heat and add heavy cream, warmed (caramel will steam and bubble up), and salted butter, stirring until smooth.
3. Let caramel cool slightly. Stir in vanilla and salt. Let cool completely. Store at room temperature up to 1 month or in refrigerator up to 2 months. Reheat in microwave 1 minute before serving.
Chewy Caramels: Line 13x9-in. baking pan with parchment paper; spray wit nonstick cooking spray. Follow step 1, increasing corn syrup to 1 cup. Follow step 2, increasing butter to 10 tablespoons. Before step 3, return saucepan to medium-high heat. Cook to boiling without stirring. Boil until amber (245 degrees), about 9 minutes. Remove from heat immediately. Follow step 3, increasing vanilla to 2 teaspoons. Pour mixture into lined pan. Cool until firm, about 2 hours. Remove from pan using parchment. Cut into bite-size pieces.
Sea-Salt Chocolate Caramels: Dip cooled Chew Caramels (above) pieces in melted dark chocolate and sprinkle each with pinch coarse sea salt; let set.
Sesame Caramels: After pouring Chewy Caramel (above) into pan, top with 1/4 cup toasted sesame seeds.
Candy Bar Caramels: After pouring Chewy Caramel (above) into pan, top with 1/4 cup finely chopped peanuts. Di cooled pieces in melted dark chocolate; let set.
Nutty Caramels: Follow instructions for Candy Bar Caramels (above), but don't coat in chocolate.