Combine the sugar and 1/3 cup water in a medium heavy-bottomed saucepan. This is the only time you can stir the sugar. If you stir it while it's cooking, it turns to rock candy. Place the saucepan over medium to low heat until the sugars start to dissolve, 5 to 10 minutes. Then turn the heat up to medium-high and cook until the sugar starts to caramelize, 5 to 7 minutes. Do not stir while this is happening. You've got to watch the pot, because it goes from caramel to burnt really quickly. And be careful, the mixture is extremely hot!
Turn off the heat and stand back to avoid splattering. Slowly add the cream. Don't panic - the cream will bubble violently, and the caramel will solidify. Just give it more time to liquefy again-trust me!
Simmer over low heat, stirring constantly, until the caramel dissolves and the sauce is smooth, about 2 minutes. Allow the sauce to cool to room temperature, at least 4 hours. It will thicken as it sits.