Before you start cooking, fill a large bowl or pot with ice water and set it aside. This will help cool the caramel quickly later. Measure out the cream, then stir in the salt and vanilla extract. Set the mixture aside so it is ready to pour in once the sugar reaches the right color.
Place the sugar in a small heavy-bottomed saucepan and set it over medium heat. On my electric stove, this is usually between 6 and 7. Start a timer for about 6 minutes, but pay closer attention to the color than the clock. You are looking for a deep amber shade, about the color of a copper penny. As the sugar heats, it will begin to melt into a clear syrup. Do not stir too early. If needed, gently swirl the pan to help it melt evenly.
This is the most important part of the recipe. When the sugar reaches that rich copper color about the shade of a copper penny and begins to give off a faint wisp of smoke, it’s ready. Be careful, it can go from perfect to burnt very quickly!
Once the sugar reaches that deep amber color, remove the pan from the heat and slowly pour in the cream mixture while whisking constantly. The caramel will bubble up fiercely, so pour slowly and be careful. At this stage, the sugar will usually clump and seize. That is completely normal.
Return the pan to low heat and continue whisking or stirring with a wooden spoon until the caramel smooths out and everything is fully combined. Keep stirring until the soft caramel chunks melt back into the sauce.
Once the caramel is smooth, place the saucepan into the ice bath and stir until it cools to room temperature. As it cools, it will thicken into a soft, creamy caramel sauce.
Pour the finished caramel into a jar with a lid and refrigerate. It will keep for about 1 month in the refrigerator or up to 3 months in the freezer.