Prepare the mushrooms: Clean and slice the mushrooms. Set them aside.
Sauté the aromatics: In a large pan, heat the olive oil and butter over medium heat. Add the chopped onion and cook until softened, about 3-4 minutes. Add the garlic and cook for another minute.
Cook the mushrooms: Add the sliced mushrooms to the pan. Stir occasionally and cook for 5-7 minutes, allowing the mushrooms to release their moisture and brown.
Toast the rice: Add the Arborio rice to the pan and stir for 1-2 minutes, allowing the rice to absorb the flavors of the mushrooms and aromatics.
Add the wine: Pour in the white wine (if using) and let it cook off for 1-2 minutes.
Add the broth: Gradually add the vegetable broth, one ladle at a time, stirring frequently. Wait until the liquid is mostly absorbed before adding the next ladle of broth. Continue until the rice is creamy and tender, about 18-20 minutes.
Finish the risotto: Stir in the Parmesan cheese, and add heavy cream (if desired). Season with salt and pepper to taste. Stir well to combine.
Serve: Serve immediately, garnished with fresh thyme or additional Parmesan cheese, if desired.