In a heavy saucepan, combine the granulated sugar, heavy cream, corn syrup, and salt. Place over medium heat and stir until the sugar dissolves.
Once the mixture begins to boil, do not stir. Insert a candy thermometer into the mixture and cook until it reaches the soft ball stage, around 235°F (113°C).
Remove the saucepan from heat, and add the butter and vanilla extract. Allow the mixture to cool for about 10 minutes without stirring.
Once cooled, begin to pull the candy. Use a wooden spoon or your hands (greased with butter to prevent sticking) to stretch and knead the candy until it becomes creamy and light in color, which should take about 10-15 minutes.
Form the candy into a log or desired shape, and place it onto a greased baking sheet.
Let the candy cool completely at room temperature before cutting into individual pieces. If desired, wrap each piece in wax paper.
Make sure to keep an eye on the temperature while cooking to avoid burning the candy.
You can add food coloring to the mixture during the pulling process for a fun twist.
Store the candy in an airtight container at room temperature for up to 2 weeks.