Wash the mushrooms and trim the stem. Slice each mushroom into three slices, each one about an inch thick.
Heat the cast iron skillet at low temperature and add a little oil. Add the mushrooms, being careful to give each slice enough room to get a sear. Stand them on their edges. Don't just throw them in the pan. Let them slowly cook down. If you do this under high heat the mushrooms will burn before they cook out their moisture. Keep the temperature low and be patient. Turn the mushrooms periodically, so all sides get a proper caramelization. The mushrooms will shrink significantly in size during this cooking process.
While the mushrooms are cooking, make the garlic paste. I like to use a mortar and pestle to do this, but if you don't have one, you can just mince the garlic. Place the garlic, salt, thyme, parsley, and about a tablespoon of olive oil in the pestle and mix to form a paste.
When the mushrooms are fully caramelized and ready to eat, add the garlic paste and two tablespoons of butter to the pan. Cook everything just long enough for the garlic to brown, but be careful not to overcook and burn the garlic.
Remove from heat and serve immediately. These can be made ahead and reheated later. I've made them at home and taken them camping. A quick toss back over the pan to reheat them and they're delicious.