Preheat a large, deep skillet over medium - medium-high heat. Add the butter. When melted, add the sliced mushrooms, stirring to coat them with the butter. Add the fresh thyme and a pinch of pepper.
Saute, stirring occasionally, until brown and caramelized. This can take 15-20 minutes depending on the size of the pan.
Meanwhile, bring a large pot of water to a boil. Add 2 teaspoons of salt and the fettuccine. Cook for one minute less than al dente as noted on package directions. Reserve 1 cup of pasta water before draining pasta. (Do not rinse pasta).
While the pasta cooks, when the mushrooms are caramelized, reduce the heat to medium. Add the heavy cream and the cream cheese. Stir until the cream cheese is melted and the cream has thickened slightly. Add the parmesan cheese and season with salt and pepper.
Add the pasta to the sauce and stir to combine. Add pasta water as necessary to bring the sauce together to fully coat the pasta and thin out the cream if needed.