Melt the butter over medium heat in a wide skillet. Add the mushrooms and cook until the mushrooms begin to brown and caramelize.
Add garlic, optional thyme, and a few twists of black pepper. Cook a minute.
Add the broth, turn up the heat, and bring to a boil. Add the fresh pasta and using tongs, stir and lift to cook the pasta, about 5 minutes. There should be a little saucy liquid left in the bottom of the skillet, if not add additional broth or water.
Add the heavy cream and stir to combine. Simmer a minute or two to thicken the sauce. Turn off the heat, add Parmesan, and toss with tongs until melted into the sauce.