To make the crust: In a food processor, combine the pistachios, sugar, and salt, and blend to a coarse crumb. Add the coconut oil (it does not need to be melteand pulse until the mixture crumbles together. Distribute the mixture between 8 serving glasses and use a muddle or the back of a spoon to press it down evenly and firmly. Set aside.
To make the malabi: In a medium bowl, whisk together ½ cup coconut milk with the cornstarch, vanilla bean paste or extract, and rosewater.
In a medium saucepan, whisk together the remaining coconut milk, the salt, and sugar and heat over medium heat until simmering, whisking often. pour in the cornstarch mixture in a slow, steady stream while whisking and then continue to heat while whisking until the mixture has thickened, 1 to 2 more minutes. Taste and adjust extracts and flavorings as desired. Divide the mixture into the 8 serving glasses (about ½ cup in each), cover, and chill for 4 hours or overnight.
To make the persimmons: 10 minutes before serving, combine chopped persimmon, vanilla bean paste or extract, lemon zest, and sugar in a medium bowl and toss to combine. Let sit a few minutes to allow the flavors to marry. Spoon on top of the malabi directly before serving.