A 3-quart (or larger) heavy-bottomed saucepan should be filled with water. With care to prevent splashing into the pan's sides, add the sugar and whisk it into the water using a fork. For approximately 6 to 8 minutes, cook the mixture over medium heat. At 320°F, the sugar will begin to melt and quickly turn into caramel. Reduce the heat to low once the sugar turns honey-colored (about 340°F), and cook it for another 5 minutes or so, or until it turns amber-colored and reaches 360°F.
After turning off the heat, add the heavy cream, salt, and vanilla extract rapidly but carefully (if using). A mesh strainer on top of the saucepan is a good idea to prevent sugar from spitting over your arms because the mixture will boil up violently. When the caramel is smooth, take the mesh strainer off.
Avoid scraping the pot's bottom as you remove the caramel from the pan. You don't want any remaining crystallised sugar to combine with your ultra-smooth caramel; there may be some there. Instead, freely pour the caramel into a canning jar or other heat-resistant container.