Add the corn meal, coconut oil, miso, and pepper. Whisk constantly for 1 minute. Once the polenta thickens you can whisk it less frequently, but make sure to continue to whisk it to avoid clumps. Cook ~30 minutes until tender, adding water as necessary.
In the meantime, heat a large pan over high heat. Add the olive oil. When hot, add the mushrooms. Don’t crowd the pan. Cook, without stirring, until the mushrooms are well browned, ~3 minutes. Sprinkle with salt and pepper. Give the mushrooms a good toss to turn them and then briefly sear on the other side.
Serve the mushrooms over the polenta, and garnish with the fresh parsley.