Place the sugar, salt, cream of tartar, and water in a deep, heavy-bottomed saucepan that holds at least 1 1/2 quarts (the syrup will bubble up as it cooks). Stir briefly to combine, then set the pan over medium-high heat. From this point on, swirl the pan instead of stirring to help prevent crystals from forming.
1/2 cup (100 grams) granulated sugar, 1/4 teaspoon sea salt, 1/16 teaspoon cream of tartar, 1 tablespoon water
When the mixture comes to a boil, reduce the heat to medium and watch it carefully. No walking away! The syrup will start turning golden at the edges. Gently swirl the pan without lifting it off the heat to even out the color.
As the syrup darkens to light amber, remove the pan from the heat as soon as you notice darker streaks. Avoid letting the sugar syrup become too dark, as it will continue to cook slightly after being removed from the heat. Darker syrup has a richer flavor, but letting it go past medium amber can result in bitter or smoky notes.
Immediately after removing the caramel from the heat, stir in the butter, one tablespoon at a time. Gradually add the heavy cream, stirring until fully incorporated. Return the pan to the heat and continue cooking until the mixture reaches 235 °F (113 °C). Remove from the heat again, stir in the vanilla, and mix until smooth.
3 tablespoons (42 grams) unsalted butter, 1/4 cup (60 ml) heavy cream, 1 teaspoon vanilla extract
Let the caramel cool in the pan on a cooling rack for 30–40 minutes. If you want it to cool faster, transfer it to a wide, shallow, heatproof container. The caramel should still be pourable but not too runny.
This caramel can be made up to 3 days in advance and stored in the refrigerator. It will firm up in the fridge, so reheat gently to make it pourable again.