Mix coconut milk, rice milk, oil and cinnamon in large bowl with wire whisk until well blended. Set aside.
Place aquafaba and cream of tartar in bowl of electric stand mixer fitted with whisk attachment. Beat on high speed until stiff peaks form, about 10 minutes. Reduce speed to low and add icing sugar and vanilla; continue mixing increasing speed as needed until well blended.
Gently stir or fold one third of the aquafaba mixture into the coconut milk mixture just until mixed. Continue with remaining aquafaba working in thirds until completely mixed, being careful not to overmix and deflate the aquafaba.
Transfer mixture to an 8-inch (20-cm) square baking dish. Wrap tightly with plastic wrap and freeze until solid, at least 4 hours or overnight. Scoop and serve with desired toppings, such as Vegan Mezcal Caramel Sauce.
Test Kitchen Tip: Aquafaba is the cooking liquid remaining after cooking legumes, such as garbanzo beans (chickpeas). You can make fresh aquafaba by cooking dried garbanzo beans in water, or simply use the liquid from canned garbanzo beans. Aquafaba is used as an egg replacement. You can whip it like egg whites for meringues or use it as a substitute for whole eggs in baked goods. 3 tablespoons (45 ml) of aquafaba is equivalent to about one egg, while 2 tablespoons (30 ml) of aquafaba is equivalent to about one egg white. One can of garbanzo beans contains about 1/2 cup (125 ml) of aquafaba.