Name: Sandy B. Ford River Twp, Michigan UP (Zone 4b) (Zone 4b-maybe 5a)
Karen, my understanding is that each green leaf that's left on the garlic plant represents one layer of covering on the bulb... so definitely leave at least 3 or 4 green leaves.
(I can't say about the elephant garlic, either... I've never grown it)
“Think occasionally of the suffering of which you spare yourself the sight." ~ Albert Schweitzer C/F temp conversion