Learn English – Which is correct: “I am drinking ice cream” or “I am eating ice cream”

We never say, I want an iced cream, or cream with ice, or cream which is iced, or anything else. We just say, I want ice cream. My point is when something is un-modifiable, that means it exists as a single unit. It may appear to have two words, but those two words, spoken separately, would have different meanings, so that particular word needs to be spoken in one breath to convey a particular meaning. So 'ice cream' is a one word. It has a distinct meaning.

Now consider, 'beautiful day.' Both Beautiful and Day have their own separate meanings and spoken together they convey a different meaning. Yet 'beautiful day' is not one word, because same can be expressed differently like, lovely day, pleasant day, awesome day, etc. More importantly, in 'beautiful day,' beautiful is an adjective. And if we start representing ice cream as having two words, would we say ice is an adjective here?

I think it's a mistake to look for a way for that sentence to make sense. I would say instead that it's supposed not to make much sense.

Evidently the narration is in a very close third-person point of view, and it's describing the character's actions with the words he would use himself -- and in this case it seems clear that it's words he actually thinks.

The borderline-nonsensical choice of "educate" serves to characterize the character as an alcoholic who's trying to tell himself he's not. He's pouring vodka over the ice, but he's pretending that he's doing that to do the ice a favor (education is a good thing!), rather than drinking because he's addicted.

The bizarre phrasing also lets him feel clever about having invented such a colorful metaphor (and clever people are too smart to let themselves slide into alcoholism; he's clever; ergo he's not an alcoholic. Phew!)

The metaphor isn't really all that clever (for one thing, it doesn't make sense), but he's already drunk enough to be unable to see that.