Warm 2 tablespoons of the olive oil in a deep skillet or Dutch oven set over medium heat. Introduce the mushrooms along with ½ teaspoon of sea salt and a generous grind of black pepper; toss well to coat. Sauté, stirring only from time to time, for approximately 8 minutes until the mushrooms are tender and browned. Remove and reserve the mushrooms, working in batches if needed.

Wipe the skillet clean and return it to the burner. Pour in the remaining 2 tablespoons of olive oil, add the onion, and sprinkle in the remaining ¼ teaspoon salt. Cook, stirring from time to time, for 5 to 8 minutes, allowing the onion to soften. Incorporate the garlic, thyme, and Arborio rice, letting them toast gently for about 1 minute before deglazing with the white wine. Stir well and cook for 1 to 3 minutes, ensuring the wine reduces.

Gradually ladle in the warm broth, ¾ cup at a time, stirring continuously and waiting for each addition to be absorbed before pouring in the next. With the final portion of broth, fold in two-thirds of the sautéed mushrooms. Continue to cook until the risotto achieves a luscious, creamy consistency and the rice remains slightly al dente. Stir in the grated cheese and adjust seasoning as needed.

Finish by topping with the reserved mushrooms and a scattering of fresh parsley. Serve immediately, offering extra grated cheese on the side if desired.