Onion: purée or powder?

My grandmother used to put in a whole peeled onion, poked through with a knife, into a dish, and then fish it out before serving. It imparts its flavor quite well.

I am the same way! It is such an important flavor component for just about every cuisine on the planet, but the texture weirds me out.

For most of my life always just blitzed it into mush, but as others have pointed out that does lead to extra liquid that you have to cook down, so just be aware. These days I am a little more tolerant, so I can just mince it very finely (like 1/8 of an inch pieces) and you don't even notice that it's there. I just cut the onion in half, slice it thinly, then chop, turning my knife so I'm always cutting perpendicular to the outside edge of the onion to create the small mince.

For some odd reason I've never had the same aversion to shallots, which was sort of a gateway food for me to handle more than onion mush. If your wife is the same kind of weirdo as me, maybe try substituting shallots?

As some folks have pointed out, it will greatly depend on a dish you are making. But generally yes, for stews, or curries and sauces, you could puree the raw onions. But that will not work in the dishes that depend on that wonderful flavor of caramelized onions. In such cases, I wonder if you could caramelize the onions first, and then puree them. I feel bad for you, it is a terrible thing to cook without onions :)

A lot of Indian recipes start out by frying a puree of onion, ginger, garlic and perhaps other such things. Traditionally, this would be done with a mortar and pestle but you should be able to do an adequate job with a blender or similar device- I wouldn't leave the puree around long uncooked, though. In some parts, onions are not used because they are associated with the cooking of meat (or so I've read), substituting a substance called Heeng (sp.?) or asafoetida. It's weird stuff; you probably don't want to go that route.

In many recipes, you can get the taste of onion by cooking it with the recipe and then removing before serving, as one does with a bay leaf or bunch of herbs.
This trick will work best, or most easily, with liquid-based dishes like soup and stew.
But even with roast beef or the like, you could put large trimmed but unchopped bits of onion (small ones whole, larger ones cut in half) in a pan, then remove after cooking.

I'll use a box grater (large holes) and just grate onion in recipes for family members (mainly grandkids) who don't want to see an onion.

When making mirepoix/soffrito/trinity, I often just put my onion, carrot, celery, garlic, peppers, etc. in a food processor and blitz the hell out of it. I try to just get a good fine mince on it, since I don't want baby food, but give it a go....after cooking it down, I don't get any texture from it.

Try using granulated onion. It's not inferior to powdered onion. Penzey's carries it.

You can pulverize it. Just understand that it has a high water content and can mess up your dish because you might have to cook it a longer time and overcook your other ingredients.