Combine sugar and water and cook on medium-high heat. Stir just until the sugar dissolves. Once sugar dissolves, stop stirring
Bring to a boil. Let caramel reach a deep amber color with a temperature of 340. I don't always use a thermometer. I just look for that amber color but if it gets too hot (past 350), it will turn bitter, so be careful.
When caramel reaches that nice, dark amber color, remove from heat, carefully whisk in the heavy cream, and swirl in the butter.
Add sea salt. Return to low heat and continually whisk until smooth.
Let it cool so that it is cool to the touch. This salted caramel thickens as it cools. If it solidifies too much before using, just reheat until you reach your desired consistency.