In a heavy 3-quart saucepan, heat the sugar over medium-high heat, whisking as the sugar begins to melt. (The sugar may clump, it's okay, it will melt back down.) Cook the sugar until it reaches a dark amber color. (Be careful, at this point it can go from perfect to burnt in a matter of seconds!)
Immediately whisk in the butter and salt until it is completely incorporated into the sugar. (Be careful the mixture will bubble and spatter.)
Remove the pan from the heat and carefully pour in the heavy cream. (Again, the mixture will bubble and spatter.) Continue to whisk until it forms a smooth sauce.
Allow to cool for 10-15 minutes before pouring into a 1-pint glass jar. The sauce can be stored, covered, in the refrigerator for up to 2 weeks.
Cook's Note: If using salted butter, reduce sea salt to 1 teaspoon.