In a heavy bottomed pot, heat the olive oil and 2 tablespoons of the butter over medium heat. Add the onion and cook until softened and translucent, 8 to 10 minutes. Add the saffron and cook, stirring, for 1 minute. Add the rice and stir with a wooden spoon until the rice is well coated and opaque, 3 to 4 minutes.
Add the wine to the rice, and then add a 4 to 6 ounce ladel of simmering broth and cook, stirring occasionally, making sure to wipe the sides and bottom of the pot clean as you stir, until all the liquid is absorbed.
Continue adding the broth a ladle at a time, waiting until the liquid is completely absorbed before adding more
About 10 minutes into the risotto process heat 1 tablespoon of olive oil in a saute pan over medium heat. Add the mushrooms and cook for 2 minutes and season with salt and pepper. Stir in the garlic, thyme, parsley and 2 tablespoons of butter then place the pan in the oven and cook for 10 minutes.
After about 20 minutes begin to taste the rice. It is ready when it is tender and creamy, but still a little firm to the bite.
Coarsely chop half of the mushrooms and garlic and stir in to the risotto with the remaining 4 tablespoons of butter and the Parmagiano-Reggiano cheese until well mixed. Transfer to serving plates and serve, topping servings with remaining mushrooms.