Place the cashews in a large bowl. Add enough room-temperature water to cover the cashews. Cover the bowl with a kitchen towel and soak overnight.
Place the bowl of an ice cream machine in the freezer overnight.
Add the cashews and soaking water to a blender. Blend, starting on low speed and increasing to high until smooth and frothy, about 40 seconds. Strain into a large bowl through a fine-mesh sieve or cheesecloth.
Reserve 1 cup (240 ml) of cashew milk for the ice cream and store the rest in the refrigerator for up to a week for another use.
In a small saucepan over medium heat, combine the water and sugar and cook, stirring constantly, until the mixture is clear, about 2 minutes. Whisk in the cocoa butter, coconut oil, and salt. Remove the pan from the heat and set aside.
In a blender, combine the cashew milk and coconut milk. Blend on low speed. With the blender running, pour in the sugar mixture to emulsify. Continue until well-blended, about 2 minutes.
Pour the mixture into a large metal bowl and mix in the vanilla extract. Scrape in the seeds from the vanilla bean and whisk to combine.
Chill the base in the refrigerator for 1 hour.
Add the chilled base to the ice cream maker and churn for 1 hour, or as long as the machine requires, until thick and creamy.
Transfer the ice cream to a loaf pan and freeze overnight.