Line a 9x9 pan with parchment paper, lightly grease and set aside.
In a large saucepan, add butter and allow to melt completely on low heat. Stir in sugar, salt, corn syrup and ONE cup of heavy cream until combined. Clip your candy thermometer on the side of the pan. Turn the heat up to medium and allow to boil gently, stirring frequently so the bottom doesn't scorch. Boil until the temperature reaches 240 degrees - at this point it should start to change color - then stir in the second cup of heavy cream. Allow the temperature to come back up but this time, to 245 degrees or "firm ball stage." Caramel should be slightly thickened. Remove from heat and stir in vanilla.
Pour caramel immediately into prepared pan. Try to refrain from scraping the sides or bottom of the saucepan because there may be some discoloration and you don't want little burnt flakes in your caramels.
Allow caramels to cool completely, up to three hours. At this point you can cut the candies into any shape you'd like and wrap them in wax paper so they stay fresh.
Soft caramels will stay fresh for up to 2 weeks wrapped in wax paper and sealed tightly in a ziploc bag.