Bring a large pot of salted water to a rolling boil. Add the rigatoni and cook according to package directions until al dente. Before draining, reserve 1 cup of the starchy pasta water. Drain the pasta and set aside.

While the pasta cooks, melt the unsalted butter in a large skillet or Dutch oven over medium heat. Continue to cook, stirring occasionally, until the butter foams, then turns golden brown and smells nutty. Watch carefully to avoid burning.

Add the sliced cremini mushrooms to the brown butter in the skillet. Increase heat to medium-high and cook, stirring occasionally, until the mushrooms release their liquid and are deeply browned and tender, about 7-10 minutes.

Stir in the minced garlic, fresh thyme, and red pepper flakes (if using). Cook for 1 minute until fragrant. Pour in the dry white wine, scraping up any browned bits from the bottom of the pan with a wooden spoon. Let it simmer for 2-3 minutes until slightly reduced.

Add the vegetable broth (or reserved pasta water) and heavy cream (if using) to the skillet. Bring to a gentle simmer and cook for 3-5 minutes, allowing the sauce to thicken slightly. Season with 1/2 tsp black pepper and salt to taste.

Add the cooked and drained rigatoni to the skillet with the sauce. Toss well to coat the pasta. If the sauce seems too dry, add a splash or two of the reserved pasta water until it reaches your desired consistency.

Stir in the lemon zest, fresh lemon juice, and 1/2 cup grated Parmesan cheese. Toss again until everything is well combined and the cheese has melted into the sauce. Taste and adjust seasoning if needed. Serve immediately, garnished with fresh chopped parsley and extra grated Parmesan cheese.