Place the freezer bowl of your ice cream maker in the freezer.
Add vegan evaporated milk and coconut milk to a saucepan, along with the granulated sugar, starch, and cocoa powder. Stir to combine. Then turn the heat up to medium-high and bring it to a simmer. The mixture will begin to thicken. Don't worry if there are lumps. Continue cooking and stirring for up to 2 minutes, allowing the sauce to thicken.
Remove from heat and allow the mixture to cool slightly, then transfer to a food processor (or blender) and pulse in short bursts until smooth.
Transfer the mixture to a sealable container and refrigerate up to overnight.
Two things need to happen before you proceed: 1) the freezer bowl of your ice cream maker needs to be thoroughly frozen (leaving it in the freezer overnight does the trick) and 2) the chocolate mixture needs to be thoroughly chilled (again, the overnight thing does the trick, but at least several hours of time in the fridge is required).
Once the mixture is chilled and your ice cream maker bowl is frozen, you’re ready to make ice cream. Spoon the chocolate mixture into the ice cream freezer bowl and churn until it reaches a desired consistency. This should take 15 - 20 minutes, but churn it for as long as possible to get enough air in the ice cream to make it light and fluffy.
Transfer the mixture to a freezer-safe, sealable container and freeze immediately.
To serve, remove the container from the freezer and allow it to sit for a few minutes at room temperature to soften. Then serve on a cone or in a cup with vegan chocolate syrup, chopped nuts, and any of your favorite toppings.