I frequently use Protobello's in a stir fry or pasta dish as a meat substitute. I find that they absorb a significant amount of oil if I put it in the frying pan. However, if I don't use enough oil, then they start to burn. Once they've gotten to a certain point, they sweat out a lot of water. However, they often end up either burnt or greasy. How can I cook them properly so that neither of those things happens?
Mushrooms DO require a good amount of oil due to the fact that they will initially absorb it.
However make sure that you're adding salt to them right away to help begin drawing the juices out and start them over high heat, making sure that the pan is "screaming" hot before you ever add the oil and the mushrooms so that it will retain the heat even after the mushrooms are added to the pan. As the juices begin to exude from the mushrooms they will take the place of the oil and as the juices evaporate, the oil will aid in browning of the mushrooms.
As they moisture begins to evaporate you can begin to decrease the temperature to avoid having to add more oil and keep them from sticking to the pan. I think mushrooms taste best when they've been allowed to cook to the point where the moisture has evaporated and a really good browning has taken place (not burnt of course).
I had another shot at portobellos last night (which prompted this question). I found that using a spray bottle to oil the mushrooms rather than just pouring oil in to the pan seemed to work much better. I'm not entirely sure why this worked, but I'm guessing that by pouring in to the pan, the mushrooms only absorb the oil on the side that's touching the pan, and the other sides may burn. When using a spray, you can evenly coat the mushrooms so that they don't absorb the oil unevenly and avoid burning.
I use an oil mister, rather than prepackaged cooking spray, so it's actually the same oil that I would otherwise just pour in the pan.
Some mushrooms are best roasted/baked in the oven. You don't need oil if you don't want it (I add bissel olive oil), just some granulated garlic and a pinch of salt. Add a bit of white wine to rescue the flavor from the pan.