Line a 13-in. x 9-in. pan with foil; butter the foil. Set aside. In a Dutch oven, combine the sugar, corn syrup and 1 cup cream. Bring to a boil over medium heat, stirring constantly. Slowly stir in remaining cream. Cook over medium heat until a candy thermometer reads 250° (hard-ball stage), stirring frequently. Remove from the heat; stir in butter and vanilla until well mixed, about 5 minutes.
Pour into prepared pan. Cool. Remove foil from pan; cut candy into 1-in. squares. Sprinkle each with a little coarse sea salt, just a few grains (6-8). Wrap individually in waxed paper; twist ends.