In a large deep skillet heat 2 tablespoons of the olive oil over medium heat. Add the mushrooms, ½ teaspoon of salt and several grinds of black pepper, then toss to coat. Cook stirring occasionally until they become soft and browned – about 8 min.
Wipe out the pan and return it to the heat. Add the remaining 2 tablespoons of olive oil, the onion and the remaining ¼ teaspoon salt. Cook stirring occasionally for 5 to 8 min until it softens. Stir in the garlic, thyme and rice and let it cook for a minute, then add the wine and cook until the wine cooks down.
Add the broth – ¾ cup at a time, stirring constantly and allowing each addition of the broth to be absorbed before adding the next. With the final addition of broth stir ⅔ of the sauteed mushrooms into the risotto. Cook until the rice has a slight al dente bite. Stir in the cheese if using and season to taste.
Top with the remaining sauteed mushrooms, garnish with parsley and serve.