Well, not really. The tears are because of the vapours released by the onion during the process of cutting it. In this little Instructable I'll show you how I cut my onions with no tears. I promise, there will be no water or fridges involved.
Step 1: The Obligatory "What You Need" List.
You will need:
* 1 or more onions.
* A cutting board.
* A sharp paring knife.
* A special note on knives *
Make sure you keep your kitchen knives sharp at all times. No knife in the kitchen is more dangerous than a blunt/dull knife. A sharp knife will ensure a true cut and will not slip or slide. A blunt knife however may easily slip from where you are cutting and cause you an injury.
Step 2: Vegetable Strip Tease.
Step 3: Hey, Cut That Out!
Start by inserting your paring knife's point into the onion to one side of this hardened area. Then carefully make a circular incision around the root (picture 3).
Bitter73 asked in the comments whether an apple corer would be suitable, rather than using a paring knife for cutting around the root in this step.
I do not have an apple corer personally, so I am not able to try this directly. However, here is the guidance I can offer.
At the base of the onion you can see the hardened root that you will be cutting around. If you look at picture 3, you will notice I have left a small distance between the edge of the root that is visible and where I made my incision. It does not translate too well in the photo as there isn't a lot to gauge sizes against, however, it is about 1/8" (approx. 3mm). So if your apple corer is a pretty standard one, and ever so slightly larger than the hardened root area, I see no reason why this wouldn't work.
(I am taking a bit of a liberty in "assuming" you will use an apple corer similar to this one. Full Disclosure: I have no prior knowledge or dealings with the company that is linked to. I used Google image search and clicked on a picture that resembled what I was thinking of. Please do not take the link being here as any form of endorsement, as it is not).
Step 4: Give Me a Lever Long Enough and a Fulcrum on Which to Place It, and I Shall Move the World.
Anyhow, your paring knife will provide you with the required lever, and the onion itself will be the fulcrum you need. Carefully insert the point of your paring knife into the incision you have made and gently lever against the root of the onion to loosen it. You'll probably need to do this all around the root (depending upon how old the onion is).
You should then be able to ease the root out of the onion in a whole piece. After which you can chop the rest of the onion however your needs require. You should now find you are able to refrain from breaking down in tears at the impending doom this onion faces.
Quick definition guide (Just for the sake of it. The definitions are both taken from the Oxford English Dictionary.
Lever: - a rigid bar resting on a pivot, used to move a heavy or firmly fixed load with one end when pressure is applied to the other:
Fulcrum: - the point against which a lever is placed to get a purchase, or on which it turns or is supported.
Step 5: The Bonus Round!
What you really need are for roots on the bottom of the onion to grow. In fact, once they are nicely grown, you can split the roots to create several onions. So keep a close eye on them and you'll soon be able to create your own supply of fresh onions.
The photo is part of our kitchen windowsill. The lettuces on the right are just the bottoms of lettuces placed in about an inch of water. At the front you can see how they start off. Whilst towards the back, shows how they look after a few weeks of growing (the biggest of the lot has been growing three weeks as of this picture.
This works for many vegetables, so give it a try. It even works with some fruit, such as pineapple.
Bitter73 asked in the comments how much of the root needs to be preserved to successfully regrow an onion.
The important thing is the little wispy white roots you see on the bottom of many onions. If you have ever left an onion in a cupboard for too long you will have seen it sprout green shoots at the top, and those wispy roots at the bottom. To avoid ambiguity for this section, "root" or "roots" will refer to those wispy white roots. "core" will refer to what you have removed from the onion.
I have only ever planted the whole core, more as a convenience than anything else. I see no reason why if you cut the base of this off and planted it, this method would be any less successful. However, you will burst into tears if you do ;)
A similar effect can be seen with "spring onions". As a general rule, people "top and tail" spring onions. That tail consists of what is principally the base of the core, that you removed from your onion. Therefore, it stands to reason that if you chopped the end of that core off, it would regrow the same way a spring onion tail does. This could prove convenient if you want to use the remainder of the core for adding flavour to your dish (by cooking with it in the pan and then removing it).
All I would say is that I haven't tried this, so I can not say with any authority that it will regrow. But if you want to give it a try, you don't have anything to lose.