Halo-Halo Partly, Part 4, Ube Ice Cream

Right, now it's time to explain what Halo-Halo is: it's Filipino for 'mix-mix' and that's pretty much what you do, and it seems with anything you want. It includes a mixture of sweet red and white beans, coconut jelly, jack fruit and other fruits (I got all this from a raid of an Asian shop and it all came in one jar) plus jelly, Ube ice cream, leche flan, crushed ice (made by crushing bought ice in a food processor where it gives its unbearable, rattling shriek) and my personal addition of a maraschino cherry. Everything then conglomerates with the addition of milk (traditionally canned evaporated milk, but whole milk for me as that's not so disgusting). The most bizarre dessert I have ever made, but really, really good fun.
Ube is sweetened purple yam puree, and despite its deep purple colour, it has a remarkably mild flavour. It's sweet with a light note of almond and vanilla. Utterly delicious. When you make this at home it doesn't give the bright purple colour that you see in Jollibee Halo-Halo, it gives a nice, mild like its flavour light grey/lilac colour.
I bought this processed from a jar, that was concerning in two ways- 1, it had a label saying 'not applicable in the UK' and 2, we had to go and see a neighbour to get it open. Another concern of mine is that, sorrowfully, the best recipe I could find (and I'm sorry to say it escapes me now where I adapted this from- to whoever came up with it thank you) used cup measures, and since I have a cute Russian Doll Set of cup measures, I didn't bother to translate. They are fairly ill-designed though. I need to get one of those pretty silver sets with handles.
1)Combine 1 cup heavy cream, 1 cup whole milk, 1 1/2 cups whole milk, 3/4 cup really good canned coconut milk (Chaokoh if you can find it) and 1/3 cup each of brown and white sugar. Bring them all gently to the boil, then take it off the heat and whisk in 1 tbsp cornflour mixed with a little of the milk. Bring it back up to the heat, don't let it boil, stirring constantly until it thickens. Transfer it to a bowl of ice water and let it cool completely before continuing.
2)If you have an ice cream maker, refrigerate that mixture overnight, if you don't, continue here. Add about 12 oz of your ube, then mix it in with a hand blender or electric whisk, until the mixture thickens slightly and the ube is mixed in as thoroughly as possible. Strain the mixture.
3)If you're using the ice cream maker, mix in the ube, put it back in the fridge to get really cold, then make ice cream to the manufacturer's instructions.
4)If you don't, don't panic. Freeze the mixture, then let it thaw again, and mix it up in the processor until fluffy again, then repeat this a few times.