Heat the broth in a medium saucepan and keep it warm over low heat throughout the cooking process.
In a large, heavy-bottomed pan, heat half the butter over medium-high heat. Add mushrooms and cook for 5-6 minutes until golden brown and their liquid has evaporated. Season with salt and pepper, then transfer to a plate and set aside.
In the same pan, heat olive oil over medium heat. Add onion and cook for 3-4 minutes until softened. Add garlic and thyme, cooking for another minute.
Add the Arborio rice and stir for 2 minutes until the grains are well-coated and slightly translucent at the edges. Pour in the wine and stir until completely absorbed.
Add warm broth one ladle at a time (about 3/4 cup), stirring frequently. Wait until each addition is almost completely absorbed before adding the next ladle. Continue this process for about 20-25 minutes until the rice is creamy and tender but still has a slight bite.
Stir in the cooked mushrooms, remaining butter, and Parmesan cheese. Season with salt and pepper to taste. Remove from heat and let rest for 2 minutes.
Garnish with fresh parsley and serve immediately while hot and creamy.