Cook pasta in salted water according to package directions. Drain the pasta, reserving ¼ cup of the pasta water.

Add 1 tablespoon of the butter and 1 tablespoon olive oil to a large skillet over medium heat. Once the butter is melted, add the mushrooms in a single layer. Cook for 3-4 minutes, undisturbed, until the mushrooms begin to brown. Sprinkle with ¼ teaspoon salt and ¼ teaspoon black pepper, toss, and continue cooking for 4-5 more minutes, stirring occasionally. Once mushrooms are tender, transfer to a clean plate and set aside.

Add the remaining 5 tablespoons butter to the skillet. Once the butter is melted, add the onion and cook for 3-4 minutes, or until translucent. Add the garlic, thyme, red pepper flakes, ½ teaspoon salt, and ¼ teaspoon black pepper. Cook for 1-2 minutes, stirring occasionally.

Pour in the sauvignon blanc and ¼ cup of the broth, turn the heat to high, and bring the mixture to a boil. Reduce the heat to medium and continue cooking for 5-6 minutes, stirring occasionally, or until the sauce is reduced by about a quarter and turns a light yellow color. Pour in the remaining ¼ cup broth and continue cooking for 3-4 more minutes, or until it turns a deeper golden color.

Remove the mixture from the heat and allow it to cool for 5-10 minutes. Transfer the mixture to a food processor or blender along with the lemon juice. Blend for 15-30 seconds, scrape down the sides, and blend for 15-30 seconds longer, or until smooth.

Pour the sauce back into the skillet along with the Parmesan cheese. Cook over low heat for 2-3 minutes, or until the cheese has partially melted. Add pasta and mushrooms to the skillet and toss until coated in the sauce. If needed, add reserved pasta water, one tablespoon at a time, to thin out the sauce. Serve with parsley and additional Parmesan cheese, if desired.