Cook the pasta according to package instructions until al dente. Drain, reserving 1/2 cup pasta water, and set aside.
Heat olive oil in a large skillet over medium-high heat. Add mushrooms and sauté for 5–6 minutes until golden and tender.
Add garlic and cook for 1 minute until fragrant.
Add chopped kale and cook until wilted, about 3–4 minutes. Season with salt and black pepper.
In a small saucepan, combine butter, heavy cream, thyme, and red chili flakes. Heat gently over low-medium heat until warm.
Stir in Parmesan cheese until melted and smooth. Adjust seasoning with salt and pepper.
Add the cooked pasta to the skillet with mushrooms and kale. Pour the garlic cream sauce over the pasta and toss to coat evenly. Add reserved pasta water gradually if needed to thin the sauce.
Cook for an additional 2–3 minutes until everything is well combined and heated through.
Serve immediately, garnished with fresh parsley and extra Parmesan if desired.