Prepare a container with a lid in which to freeze the ice cream. Large yogurt containers work well (you'll need quite a few), or you can re-use a plastic ice cream tub.
Place the eggs and sugar in a food processor, mixer, or blender. Process about 1.5 to 2 minutes.
Pour this mixture into the top of a double-boiler and place over medium-high heat.
Cook for 8-10 minutes, stirring continuously with a whisk, until the mixture thickens and becomes creamy (it should look like custard). Place in the refrigerator to cool.
Pour heavy cream into your food processor, blender, or mixer. Blitz until cream becomes very thick and stiff peaks form (approximately 1 minute). Scoop into a large mixing bowl.
Fold coconut milk plus flaked coconut (if using) into the whipped cream, stirring to combine.
Now add the cooked egg/sugar mixture from the refrigerator. Also add the flavoring (vanilla/ccconut), gently stirring everything together by hand. You should end up with a thick, ivory-white batter-like mixture. Pour into prepared container(s). Set in the freezer and allow to freeze at least 8 hours, or overnight.
To serve, dip an ice cream scoop in warm water and scoop the ice cream into bowls. For extra coconutty flavor, top with a little sweetened flaked coconut. ENJOY!