I've been growing this stuff for many, many years. I love these things. First, you always plant garlic in the fall, September or October is usually fine. It overwinters great - always good to get a little growth going before it gets chilly. By the time you are moving in July, you should have harvested all of the garlic, probably by late May, early June, in zone 8. Just like other garlics, once about half the tops are yellowing and fading they can be harvested. Dig carfully from underneath (rather than just pulling up) in order to collect all of those little buttons you can find. I like seeing the tall elephant garlic flowers so I always keep a few to look at, but for the most part I remove the stalks before they get too large. I eat those scapes I cut off as well, sauteed and cooked into an omelet or something. I really don't want the plant expending energy on the flowers when I'm trying to get garlic. The garlic you dug up looks great, but it will be even better after about another month of growing.

The buttons: I save all the buttons and smaller round garlic heads(without cloves) to plant in the fall. The butons will take maybe three or four years to make a large head of garlic. I started getting a little frustrated with the buttons because they won't all necessarily sprout the year you plant them, but that doesn't mean they won't sprout the next year. To get around the problem of having random garlics sprouting when I've dug in more compost, etc., I started planting all the buttons in cheap gallon plastic pots that I bury in the garden. That way, when a number of them sprout and are 4 to 6 inches tall, I dump the pot out in my empty wheelbarrow, separate the sprouted buttons, then return the potting soil, unsprouted buttons, and new buttons, and put it right back in the garden. With the buttons, I don't even necessarily stick with the traditional garlic planting times, putting the newly dug ones right into the pots. The sprouts I separate and plant probaly 4" apart in rows, knowing they will not achieve full size in that first year. At harvest time end of May/early June, these will be what I call "rounds." The rounds will be planted in the fall for the next years' monster heads.

I've been doing this for a while, so I have enough going that I eat just about all of the monster heads that make nice big cloves. Those I allow to dry and cure a bit at harvest, clean them up, brush off dirt, and put them in a cardboard box. I also harvest quite a few Rounds - I take whole folded newspaper sections, staple along two edges (with the fold on the third edge it makes a bag), put a "not-too-crowded" amount of rounds in each bag(maybe a pound or two), and staple the open end shut. I label it "Rounds" with my sharpie, and store until fall. Because 6, 8, 10 sheets of newspaper blocks light, and because I let them cure and dry some before packaging, removing excess dirt and roots, I've actually had some of my stored garlic last more than a year to a planting season, though not something desired.

I've also stored the buttons that way as well, but I've gone away from it because if they can last in the ground for two or three years without sprouting, why should I wait until fall to get them in the ground. I just like having control, so I use the buried pots.

Eating and handling a very large garlic clove is no different than how you would deal with a large onion you don't eat all of in one sitting. I have a very small covered container with a tight fitting lid that I may peel several cloves and put in. If I only use half of a particularly large clove, I just put the other half back in the container for next time. These are very mild compared to regular garlic, so I use a lot in most things. I love it though. I grow other garlics, and like them just fine, but dealing with the little cloves will often just take me back to my elephant garlic that I have been continually propagating, starting in Texas, to Virginia, to Maryland, to New Jersey, and back to several different houses here in Virginia, since the mid-1980's.

Hope that helps.