Add the sugar, water, and corn syrup to a stainless steel saucepan. Whisk together briefly to combine, then place over low heat.
Don’t stir it anymore once it’s on the heat. If you have any dry spots, you can slowly move the pan in a circular motion to gently swirl the liquid. Heat until it is simmering and the sugar has dissolved - you’ll know because the mixture will turn clear instead of cloudy, just like with simple syrup.
Once the sugar has dissolved, turn the heat up to medium and let it bubble - don’t stir or swirl it at all after this point. If you notice any sugar crystals forming on the side of the pan, you can use a pastry brush dipped in water to ‘paint’ them with water so they slide back into the caramel in a liquid state.
You’ll see the syrup start to thicken, and the bubbles will become slower. Eventually, it will start to change color - don’t take your eyes off of it at this point, as it can go from ready to burnt very quickly. Once it reaches a deep amber color, remove it from the heat. If you want to use a thermometer for absolute accuracy, caramel should reach 340°F / 165°C.
Add the butter, one chunk at a time, whisking until melted. It may froth up a bit if the butter is cold.
Slowly pour in the heavy cream while whisking until it is all incorporated. It may also bubble up as you add it, so be careful. Then add the salt and whisk it in.
Return the pan to the heat and simmer for 1-2 minutes, whisking constantly, but slowly.
Remove from the heat and let the caramel cool in the pan for 10-15 minutes before transferring to a jar or heat-safe container. It will still be quite runny, but it will thicken as it cools.
Notes
The corn syrup is an invert sugar, which will help the sugar molecules to behave and discourage them from crystallizing. If you don't want to use corn syrup, you can use liquid glucose or golden syrup. Alternatively, you can add ½ teaspoon lemon juice or cream of tartar - this won't have the same effect but it will help. Do not stir the caramel at all once it is on the heat; this can lead to crystallization. See my section about how to avoid crystallization for perfect caramel every time.