Add the sugar and water to a 3-quart heavy bottomed saucepan; stir a little so it sits in a flat, even layer.
Warm pot over medium heat and cook until the sugar dissolves, turns clear, and starts to bubble. (It will be cloudy at first, but will turn into a clear, bubbling liquid.) This takes about 3-4 minutes.
(At this point, do not stir again - simply allow to bubble, swirl the saucepan occasionally and brush down the sides of the pan, as needed, to prevent crystallization.)
Sugar will form clumps, but continue swirling and cooking until the mixture thickens and turns a deep amber color like honey (this can take anywhere from 8-12 minutes), keeping a watchful eye so the mixture doesn’t burn.
Carefully add the butter and whisk until completely melted. (The caramel will bubble up rapidly, so be careful and continue to whisk.)
Remove the saucepan from the heat and slowly pour in the cream, whisking continuously until all of the cream has been incorporated.
Whisk in the vanilla and salt.
Set aside to cool in the pan for 10 minutes.
Then pour into a lidded glass jar and allow to cool completely. (It will thicken as it cools.)