Pour the sugar and water into the saucepan; stir before heating to ensure the mixture is an even flat layer.
Cook the mixture on medium heat until the sugar is completely dissolved and the mixture starts to bubble and turns clear. This will take 3–4 minutes.
Allow the mixture to continue bubbling for the next 8–12 minutes, all the time swirling the saucepan and brushing down the side if need be so that it does not burn or crystalize.
The mixture may form clumps, but let it cook until it turns into a thick, deep amber-colored liquid, more like honey.
Add in the butter and whisk with your spoon until it completely melts into the mixture. (Caution: the caramel will bubble more rapidly as you do this, so be more careful.)
Turn off the heat or remove the saucepan from the heat and whisk in the cream until smooth.
Add and whisk in the vanilla extract and salt.
Allow it to cool for about 10 minutes before transferring it to a storage jar and allowing it to cool completely before covering and refrigerating the sauce. The sauce thickens as it cools.