I was making vegan coconut ice-cream with coconut milk base. Instead of using a can of coconut milk, shredded coconut with hot water was squeezed through a towel for coconut milk replacement. Then almond milk added and whisked together before putting in the back of the refrigerator (no ice cream maker). Ice cream is really hard and icy after one night. Is it possible to make creamy and soft coconut ice cream with coconut milk from shredded coconut or coconut flesh?
As you froze the base without agitating it, larger ice crystals would have formed.
If you have a food processor, you may be able to rescue it by cutting it into chunks (to fit in the food processor), then whizzing it around 'til it's more like a smoothie, then re-freezing it.
If you don't have a food processor, you might be able to let it thaw completely, then re-freeze it, making sure to agitate it multiple times in the process. One easy way to do it i to put it in a heavy zip-top bag, then a second one (double bagging it), then you can just shake & squish it around every so often while it re-freezes.
Perhaps a cornstarch base to help thicken the mixture might help. Also the advice about taking it and whisking is very important.