These soft and creamy caramels are rich and buttery. They're not hard to make, but you do need a candy thermometer; if the caramels aren't cooked to the correct temperature, they won't be chewy. Once you learn to make them, experiment by adding spices or other flavors to the molten caramel like cinnamon, cayenne, or bourbon.
Line an 8-inch square baking dish with parchment paper, allowing some to hang over each side. Then, brush the parchment paper 1 tablespoon of the butter.
Combine the water, sugar, and corn syrup in a deep, heavy saucepan. Heat the mixture over medium-high heat until it is a light golden brown. If you notice that the sugar is browning unevenly, gently lift and swirl the pan, but do not stir it (stirring can cause the sugar to crystallize).
At the same time, combine the cream, butter, and fine salt in a small saucepan and bring the mixture to a simmer over medium-low heat. Be sure to watch the cream; if it looks like it is going to bubble over, reduce the heat. As soon as the mixture comes to a simmer, take the pan off the heat and set it aside.
When the sugar mixture is ready, take it off the heat and add the cream. After the pan stops bubbling, add the vanilla and gently stir the caramel with a wooden spoon.
Attach a candy thermometer to the side of the pot, return the caramel to the heat, and continue cooking the caramel until it reaches 248 degrees.
Very carefully pour the caramel into the prepared pan and put the pan in the refrigerator to cool, about 3 to 4 hours.
When the caramel is cold, remove the parchment and caramel from the pan and place it on a cutting board. Cut the caramels with a sturdy knife whose blade has been rubbed with butter or vegetable oil to prevent it from sticking. Sprinkle the caramels with coarse salt and wrap each in a small piece of waxed paper.
Store the finished caramels in the refrigerator and allow them to come to room temperature before eating them.