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Originally Posted by ED BUCHANAN  Sure you can poach in oil. Right now big thing is Lobster poached in Butter a la T.Keller. 
There is frying and then deep frying all done by temps and control. |
Sure, that's why I asked why the OP wants to do this. As far as I understand it, gentle poaching in fat (butter, oil, whatever) will in effect replace the water in the poached object with the fat. If you poach lobster in butter, it becomes insanely creamy and buttery, and retains its natural texture. If you poach an old hen in oil, the hard cartilage breaks down and the flesh gets tenderized -- not health food, to be sure, but much tastier than a stringy old hen.
But tofu is basically a sponge filled with water. If you gently poach it in oil, it will be a sponge filled with oil. The flavor of tofu is extremely mild and tends to degrade somewhat the longer you cook it; when it gets cooked a long time in China, for example, it's usually served with the cooking liquid as a soup. So I'm afraid that poaching tofu in olive oil long enough to achieve much of anything is going to produce a cube of olive-oil flavored squodge. I suppose you might then spread it on toast or something, but what's the point?
Thus my question. Why do you want to do this? What result are you trying to achieve? I could very well be missing the point, or mis-predicting what will happen. Can you describe the intended result? Then we can help try to figure out how to achieve it.