Warm 2 tablespoons of the olive oil in a Dutch oven or large, deep skillet over medium heat, then add the mushrooms with ½ teaspoon salt and several grinds of pepper. Cook for 8 minutes, stirring occasionally, until the mushrooms are soft and browned; work in batches if the pan looks crowded, then set them aside.

Wipe out the pan, heat the remaining 2 tablespoons olive oil, and cook the onion with the remaining ¼ teaspoon sea salt for 5 to 8 minutes before adding garlic, thyme, and rice for 1 minute. The onion should be soft, and the rice should crackle lightly with translucent edges before you pour in the wine and cook it for 1 to 3 minutes until mostly absorbed.

Add warmed broth ¾ cup at a time, stirring continuously and waiting until each portion is absorbed before adding more; stir in two-thirds of the mushrooms with the final addition. The risotto is ready when the grains are creamy with a slight al dente bite and the spoon leaves a glossy trail through the pan.

Stir in the cheese, taste, and adjust the seasoning, then divide the risotto among bowls and finish with the reserved mushrooms, parsley, and more cheese if desired. The finished risotto should settle into a soft, flowing pool rather than stand in a stiff mound.