In a medium saucepan, combine the coconut milk, sugar, sea salt, and vanilla extract. Heat over medium heat, stirring occasionally until the sugar is completely dissolved. Do not let it boil.
Remove the saucepan from heat and stir in the lime juice. Allow the mixture to cool to room temperature.
Once cooled, pour the mixture into a blender and blend until smooth.
Transfer the blended mixture to an ice cream maker and churn according to the manufacturer’s instructions until it reaches a soft-serve consistency.
Fold in the chopped peanuts, then transfer the sorbet to an airtight container.
Freeze for at least 4 hours or until firm.
Before serving, let the sorbet sit at room temperature for a few minutes to soften slightly for easier scooping.