In a 3-quart heavy-bottomed saucepan, combine the sugar and water. Stir the mixture just enough to ensure a uniform, level coating.

Cook sugar in a warm pot over medium heat until it dissolves, turns transparent, and begins to boil. (At first it will be hazy, then it will clear up and become a clear, bubbling liquid.) This takes roughly three to four minutes.

(At this point, do not stir again; merely let the mixture to bubble, intermittently swirl the pan, and brush down the pan's sides as necessary to avoid crystallization.)

Although the sugar will clump, keep stirring and heating until the mixture thickens and gets a rich amber color, like honey (this can take anywhere between 8 and 12 minutes). Keep an eye on the mixture to ensure that it doesn't burn.

Add the butter slowly and whisk it in until it is totally melted. (The caramel will bubble up quickly; take caution and keep whisking.)

After turning off the heat, add the cream slowly while continuing to whisk until all of it has been integrated.

Salt and vanilla are whisked in.

Allow the pan to cool for 10 minutes.

Then pour the mixture into a glass jar with a lid and let it cool fully.