Pour cream into a heavy saucepan, and swirl up all sides. Add 3 cups sugar, butter, cream of tartar, and salt, and stirring constantly, bring to a boil over medium-high heat. Stir in corn syrup. Then wash down sides of pan and the spoon.

Before the mixture reaches 240 °F, Melt and caramelize the remaining ½ cup sugar over high heat, in a separate heavy pan. As soon as it becomes completely dissolved and caramel colored, remove from heat, and carefully pour it into cream mixture, stirring carefully to ensure that it is all incorporated. Cook over medium heat until it reaches 240 °F.

Pour onto marble slab (do NOT scrape the sides of the pan), and allow to cool enough to touch and handle. Add vanilla. Beat and knead with a bench knife, wooden spoon, or your hands until it loses its shine, and becomes the texture of smooth fudge. Work in chopped pecans, if desired, and shape into logs or squares. Wrap tightly with plastic.