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Raw onions are lot like Björk's music: I recognize their inherent value, and in a limited set of cases I absolutely love them, but more often than not my impulse is to say...uh, no thanks.
In Björk's case—and this is pure speculation on my part—I've long suspected that she's at her best when a good producer is there to rein in her more peculiar impulses, keeping at least one foot of her musical genius solidly grounded. Raw onion requires a similar level of careful direction on the part of the cook. When handled recklessly, its pungency can easily overpower the food it's served with, leaving me, at least, with a bad taste in my mouth.
There are many ways to tame an onion, aside from cooking it, of course. One is to consider the type of onion you're starting with, perhaps choosing a sweeter tasting, less sulfurous variety like Vidalia or Walla Walla; white and red onions also tend to be more mild than yellow, and are therefore often better choices for raw applications.
Another option is to make sure to use a sharp knife when cutting the onion, which reduces the amount of cellular damage that unleashes enzymatic reactions responsible for an onion's sharp aroma and flavor. The ratio of the onion to other ingredients also makes a difference (less onion, obviously, means less overall pungent onion flavor), and the size and method of your slicing matters too—thinner slices and smaller diced bits are more pungent due to more cells being split open, and orbital slices smell more strongly than pole-to-pole ones for the same reason. Yet another trick is to wash the sliced or diced raw onion with water, which rinses away the pungent fluids while keeping the onions crisp. (You can read more about these factors here.)
One of my favorite tricks, though, and the one I turn to again and again, whether I'm making salads or sandwiches, is to rapid-pickle my onions in vinegar.
What do I mean by rapid-pickle? It's not an official cooking term, really; I made it up to emphasize just how fast the method is. Usually, people talk about quick-pickling, and if I were being accurate, I'd call this a quick-pickle too. But quick-pickling, while still an easy method, still suggests at least a small amount of work: for our quick-pickled red onions, you have to make a brine that balances vinegar with sugar and salt. Some recipes require mixing in just enough water to keep it from being too tart or adding various aromatics like the peppercorns, allspice, and bay leaves in our Yucatán-style pickled onions. It's also common to heat up a brine, pour it on the vegetables, and then let them cool. Quick-pickling is far quicker than a fermentation-based pickle, which can take several days or weeks, but it still requires some advance planning.
Not these "rapid-pickle" onions. Nope, they couldn't be faster or easier. All you do is cut up your onion into slices or dice (I prefer slices and rings for layering on sandwiches, and dice for tossing into bean salads and the like), then pour enough vinegar on them to cover. That's it. Then you just have to wait long enough for the vinegar to do its job, rinsing away the harsh sulfurous compounds, softening the onion, and giving it a pleasantly tart pop of flavor.
If you use red wine vinegar, my personal favorite, the onions also turn an amazing hot-pink color. At a minimum, this takes about 15 minutes, though you can safely leave the onions in the vinegar for at least an hour, if not more, with the onions gradually softening and becoming more tart as they marinate.
The above photo shows the onion rapid-pickling process in 15-minute increments, starting on the top left at zero and ending on the lower right at an hour and a half. You can see how quickly the changes set in, and then intensify.
Then, whenever you're ready for them, just drain and add your pickled onions to whatever it is you're cooking, like the steak sandwich above. The result is a bold oniony character that's tempered by a tart vinegary pop, like raw onion and pickle rolled into one.
And that color...it's...All Neon Like.