Pour the tablespoon of olive oil into a large sauce pan and heat on medium for about 30 seconds. Add the diced onion and cook, uncovered, until translucent, about 5-7 minutes.
Move onions to the outside of the pan and put both kinds of mushrooms into the middle of the pan. Cook, uncovered, for about 5 minutes.
Stir mushroom and onions together and add thyme. Cook, covered, for another 10 minutes. Notice that substantial amounts of moisture will come out of the mushrooms and they will lose about half of their size.