Chill coconut milk in the fridge at least 3 hours, ideally overnight. Make whipped coconut: Spoon coconut cream into a large bowl, leaving liquid in can, and use a hand mixer to beat coconut cream until very creamy. Set aside.
Make whipped cream: In a separate large bowl using a hand mixer (or in a bowl of a stand mixer), beat heavy cream until soft peaks form. Beat in sweetener and vanilla.
Fold whipped coconut into whipped cream, then transfer mixture into a loaf pan. Freeze until solid, about 5 hours.