In a small, heavy saucepan, slowly combine the sugar and water, taking care not to let any of the mixture splash up onto the sides of the pan.
Cook the mixture over low heat until the sugar is mostly dissolved, stirring slowly (so sugar crystals don't splash up the sides of the pan).
Increase the heat to medium and bring the syrup to a boil. Cover the saucepan and let the syrup boil for 2 minutes.
Uncover, reduce the heat to medium, and continue to boil, without stirring, until the edges start to turn golden brown. If there are hardened sugar crystals on the sides of the pan above the sugar mixture, wash them down with a wet pastry brush.
Continue cooking until the syrup turns a deep amber brown (see the pictures in the post), about 5-7 minutes. It will take more or less time depending on the heat of the stove, so watch closely.
Remove from the heat and add the butter. Gently stir until the butter is fully melted. Stir in the cream. If the sauce becomes lumpy and isn’t whisking together, set the pan over low heat and stir until smooth. Stir in the vanilla and salt. It will bubble when the vanilla is added.
Let the sauce cool until warm before transferring to a jar or other container to store in the refrigerator. Reheat on low on the stove or in the microwave as needed.