Preparation Add the bowl and paddle of your ice cream maker to the freezer and allow to freeze over night.
Add the heavy cream and coconut milk to a saucepan over medium heat and heat to a gentle simmer.
Whisk the egg yolks and swerve together, then set aside.
Temper the eggs with the cream- add a ladle full of the cream to the egg mixture, whisking the whole time.
Add another ladle full of cream, then add the mixture into the saucepan with the cream and cook on medium-low for about 8-10 minutes (stirring constantly), or until the custard thickens and coats the back of a spoon and stays separated.
Remove from the heat and whisk in the salt and vanilla and coconut extracts and allow to cool for a few minutes.
Cover with plastic wrap, making sure the plastic is touching the custard, so it doesn't form a skin.
Chill in the fridge for at least 1 hour or over night.
Its important to make sure the custard is very cold before adding to the ice cream maker, so the longer it chills, the better.
Remove the chilled custard from the fridge, stir in the lime zest and pour into your ice cream maker.
Churn for 25-30 minutes, according to the instructions on your ice cream maker (mine took 25 minutes).
Once its the consistency of soft-serve, its ready! Store in the freezer.