Place granulated sugar in a medium-sized, heavy-bottomed saucepan over medium heat. Stir continuously with a heat-resistant spatula or wooden spoon until the sugar starts to melt.
As the sugar continues to melt, it will clump. Keep stirring until it transforms into a smooth, amber-colored liquid. Be cautious as the sugar can burn quickly; reduce heat if necessary.
Once the sugar is fully melted and has turned into a caramel color, add the unsalted butter gradually. Stir continuously to incorporate the butter into the caramelized sugar.
Slowly pour in the heavy cream while stirring constantly. The mixture will bubble, so be cautious. Continue stirring until the caramel sauce is smooth and well combined.
Remove the saucepan from heat and stir in the vanilla extract and sea salt. Taste the caramel and adjust the salt level according to your preference.
Allow the caramel sauce to cool for a few minutes before transferring it to a heatproof jar or container. Once cooled, seal the container and store it in the refrigerator for up to two weeks.