Whisk one cup of the water (chilled, Note 1) together with the cornstarch in a small saucepan and place it over medium heat. Heat the mixture up, whisking frequently, until it comes to a simmer and thickens. Immediately remove the pot from heat and let it cool.
Place the remaining 2 cups of water into a high-powered blender and add the cornstarch mixture, cashews, sugar, cocoa powder, corn syrup, vanilla, salt, and rum (if using). Blend until completely smooth. Run the machine a bit longer than you think you need to.
If blending has warmed up the mixture, allow it to cool before churning. Once cool, place the mixture into the bowl of a 2-quart or larger ice cream maker and churn until creamy and partially frozen, but not solid, about 25 minutes.
Stir the mini marshmallows, almonds, and chocolate chips into the ice cream by hand, then transfer it to storage containers. Freeze until fully set, about 4 hours.
Let the ice cream sit out for about 15 minutes before scooping, or briefly warm it in the microwave (Note 2). Serve and enjoy!