In a Dutch oven or large skillet, heat 2 tablespoons of olive oil over medium heat.
Add the mushrooms, ½ teaspoon of salt, and a few grinds of pepper, tossing to coat.
Cook for about 8 minutes, stirring occasionally, until the mushrooms are tender and browned.
Remove them from the pan and set aside.
If needed, cook in batches.
Next, wipe the pan clean and return it to the heat.
Add the remaining 2 tablespoons of olive oil, along with the onion and ¼ teaspoon of sea salt.
Cook, stirring occasionally, for 5 to 8 minutes until the onion is soft.
Add the garlic, thyme, and rice, cooking for an additional minute before pouring in the wine.
Stir and cook for 1 to 3 minutes, allowing the wine to reduce.
Gradually add the broth, about ¾ cup at a time, stirring continuously and letting each addition be absorbed before adding more.
When you add the final portion of broth, mix in two-thirds of the sautéed mushrooms.
Continue cooking until the risotto is creamy and the rice is slightly al dente.
Stir in the cheese and adjust the seasoning.
Serve topped with the remaining sautéed mushrooms, garnished with parsley, and offer extra grated cheese on the side if desired.