Grease an 8x8-inch baking pan and set it aside.
In a medium saucepan over medium-high heat, combine the sugar, corn syrup, butter, and ¼ cup of cream. Stir continuously and bring to a boil.
While continuing to stir, add the remaining cream. Insert a candy thermometer and keep stirring as the mixture heats to the soft ball stage, around 240°F. The sugar syrup will become transparent and boil rapidly.
When the mixture reaches 240°F, remove it from the heat and stir in the vanilla extract. Pour the caramel into the prepared baking pan.
While the caramel is still warm, use a toothpick to pop any air bubbles that rise to the surface. Let the caramel cool overnight.
Once cooled, use a thin knife or small offset spatula to loosen the caramel block from the pan. Transfer the block to a cutting board and cut it into your desired size and shape. Wrap each piece individually in wax paper if desired.