In a large pot, melt 2 tablespoons butter. Add mushrooms and onions. Cook for 6-7 minutes until caramelized. Add garlic and cook for 1 more minute. Remove vegetables from pot.
Add remaining 2 tablespoons of butter. Add the rice, thyme and salt. Stir together and cook for 1 minute, toasting rice. Add in 1/2 cup of broth and scrape up any browned bits from bottom of pan. Add remaining broth and bring mixture up to a simmer. Turn heat to low, cover and cook for 15 minutes.
Remove pot from heat. Stir in mushrooms and onions. Cover and let stand for 5 minutes. Taste and adjust seasoning. Sprinkle with chopped parsley if desired.