Add sugar to a medium or large-sized saucepan set over medium-high heat. Using a whisk, stir constantly as the sugar begins to clump and then melt. This will take 3-5 minutes. (Note: the whisking isn’t entirely necessary, but it will help the sugar caramelize evenly).
Once the sugar is completely melted, it will quickly begin turning a dark amber color. This is the critical moment, as caramel can become overly bitter very quickly.
Carefully and gently add in the butter. It will sizzle and bubble up, so watch your hands. Whisk until the butter is completely incorporated, approximately 20-30 seconds. Turn the heat to low and whisk in the cream in 2-3 slow pours. The mixture will bubble up again so be cautious. Remove from the heat and whisk in the salt. The caramel will thicken as it cools; if needed, you can speed up this process by placing the pot over an ice bath and stirring the caramel.
The sauce can be refrigerated for up to one month. Reheat in the microwave in 30 second increments, stirring each time, until the sauce is room temperature or slightly warm, but not hot.