In a heavy-bottomed saucepan, whisk together the heavy cream and granulated sweetener over medium heat.
Bring the mixture to a gentle simmer while whisking continuously to ensure the sweetener is fully dissolved.
Reduce the heat to low and simmer for 15 to 20 minutes, whisking occasionally, until the liquid has reduced by approximately 50 percent and coats the back of a spoon.
Whisk in the unsalted butter until completely melted and emulsified into the cream mixture.
Remove the saucepan from the heat and stir in the vanilla extract and sea salt.
Allow the mixture to cool at room temperature for 30 minutes; the viscosity will increase significantly during cooling.
Transfer the finished product to a glass jar and refrigerate for up to 2 weeks.