Heat 2 tablespoons of the butter in a large saucepot over medium heat. Add the onion and saute until translucent, about 10 minutes. Add the rice and toast while stirring until it begins to smell nutty, about 1 minute. Add the chicken stock and bring to a boil, then reduce to a simmer, cover and cook on low until the water is absorbed, about 40 minutes.
While the rice is cooking, heat the remaining 1 tablespoon butter along with the oil in a large skillet over medium-high heat. Add the button mushrooms, shiitake mushrooms and thyme and cook, stirring often until they begin to brown, about 10 minutes. Add the garlic, season with salt and pepper and cook until the garlic is fragrant, about 1 minute more.
When the rice is cooked, fluff with a fork and gently fold in the mushrooms. Add to a serving bowl and sprinkle with the parsley before serving.