Add the sugar and water to a 3-quart saucepan; swirl the pot so the sugar is a flat, even layer.
Heat the sugar & water 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 the mixture to bubble, swirl the saucepan occasionally, and scrape down the sides of the pan with a heat-proof rubber spatula, as needed, to prevent crystallization.)
Sugar will form clumps, but continue swirling and cooking until the mixture thickens and turns a medium amber color (think honey-colored about 8 minutes).
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 slightly.
Pour into a lidded glass jar (we like pint-size mason jars from Amazon). Caramel will thicken as it cools.