Bring a large pot of water to a boil for pasta.

Heat EVOO and butter in large skillet over medium heat. Add mushrooms and thyme, and cook to tender, stirring occasionally, until lightly browned, 10-12 minutes. Season mushrooms with salt and pepper, and add shallots and garlic. Saut another 4-5 minutes then deglaze the pan with sherry or Marsala. Stir in cream and bring to a bubble then reduce heat to low and simmer. Season with nutmeg. When pasta is just about done, turn off heat and stir in cheese, a couple of handfuls. Cover and reserve.

Cook pasta to al dente. Reserve 1 cup starchy cooking liquid, then drain pasta and return to hot pot with peas. Add 1/2 cup cooking liquid and mushroom sauce, and toss to combine, 1-2 minutes. Add more water as necessary to coat pasta evenly.

Serve in shallow bowls topped with parsley and pass more cheese at table.