Add the granulated sugar to a medium heavy-bottomed stainless steel saucepan. Place the saucepan over medium-low to low heat. Stir the sugar constantly using a wooden spoon. The sugar will begin to clump, melt, and slowly turn a light golden-brown color. Scrape down any sugar crystals from the sides of the saucepan and break up any large clumps of sugar with the wooden spoon.
Continue to cook stir until all the sugar is melted, which will take about 10 to 15 minutes. Do not walk away from the stove because the caramel can easily and quickly burn. Once all the sugar is melted and the mixture turns a golden-brown color, immediately remove the saucepan from the heat.
Quickly and carefully pour in the room temperature or slightly warm heavy cream and mix well. If you do not mix immediately, the caramel can seize up. (As you add the cream, the caramel will bubble and steam. Be careful to not burn yourself on the steam.)
Add in the cubed, room temperature unsalted butter, one cube at a time, and mix well until fully melted. (As you add the butter, the caramel will bubble and steam. Be careful to not burn yourself on the steam.) Then, add in the vanilla extract and sea salt and mix until well combined.
Pour the salted caramel sauce into a heat-proof bowl or container and allow to cool to room temperature before using. If using at a later time, store the salted caramel sauce in an airtight container in the refrigerator.