Make the caramel sauce: In a small saucepan set over medium heat, add the cream and heat until warm. In a separate medium saucepan set over medium heat, add the sugar and cook until the sugar is melted and turns light gold in color, 7 to 10 minutes. Gradually whisk in the heated cream, a little at a time, whisking after each addition to avoid any lumps. Once all the cream is incorporated, remove the pan from the heat and whisk in the butter and salt. Cool the caramel slightly or, if using later, cool the caramel completely and transfer to an airtight container. Store the caramel in the refrigerator for up to 1 week.
Make the sipping caramel: In a medium bowl, add the cream and whisk until soft peaks form. In a small saucepan set over medium-low heat, add the prepared caramel sauce and the half-and-half. Cook, whisking constantly, until the caramel is melted and the drink is hot and frothy. Stir in the mezcal.
Pour the sipping caramel into 4 small heat-safe glasses and top with the whipped cream, sprinkle with sea salt and serve warm.