In a large skillet, heat 3 tablespoons oil over medium heat. Add shallots and cook until just soft, but not brown, about 3 minutes. Add 1/4 cup wine and cook, stirring constantly, for 1 minute. Add rice and stir and cook until it begins to turn translucent, about 2 minutes. Stir in thyme. Scrape rice and onion mixture into slow-cooker. (Set skillet aside and do not wash.) Turn slow-cooker to high and add broth. Cover and cook on high until tender and moist but not soupy, about 1 3/4 hours to 2 1/2 hours.
Meanwhile, using the same skillet, heat remaining 1 tablespoon oil and butter together over medium heat. Add mushrooms and cook, stirring occasionally, until mushrooms release their liquid, about 4 minutes. Add remaining 1/4-cup wine and stir and cook another minute or two to allow some of the wine to evaporate. Remove from the heat and allow to cool slightly, before placing the mushrooms in a microwave-safe bowl, cover and refrigerate. Just before rice is done, remove mushrooms from refrigerator and microwave, uncovered on high, until heated through, about 2 minutes.
Uncover the risotto and stir in the half and half, parmesan, salt and pepper to taste. Top with the heated mushrooms and sprinkle top with chopped parsley.