Step 1

Put dried porcinis in a small bowl, if using. Pour enough hot water over to cover (about 1 cup). Soak for 30 minutes. Place cheesecloth, coffee filter or paper towel in a strainer. Pour mushrooms into strainer. Reserve broth. Remove mushrooms from strainer, rinse and pat dry. Cut into bite-size pieces. Set aside.

Step 2

In a large, deep skillet or braising pan, melt butter and oil over medium-high heat. Sauté the mushrooms until lightly browned, about 3 minutes. You will have to do this in batches, so cook the oyster and king trumpet mushrooms separately from the others. Add more butter and oil as needed. Season with salt and pepper. Combine the creminis and shiitakes along with all the juice. Combine oyster and trumpet and set aside.

Step 3

Add more butter and oil to the pan. Heat over medium heat. Sauté shallots and leeks until softened. Add garlic and sauté for 2 to 3 minutes. Stir in tomato paste and cook for another 2 minutes until tomato paste is caramelized and dark brown. Stir in thyme and red pepper. Stir in cremini and shitake mushrooms, with their juices, the porcinis and the white wine. Cook, stirring occasionally, until wine is reduced by a third. Pour in 1/2 cup of the porcini water and the chicken or vegetable broth. Simmer for 3 to 4 minutes. Taste for seasoning. If too watery or bland, continue to simmer for another few minutes. Set aside (this can be prepared ahead and reheated).

Step 4

Bring 4 quarts of water with 2 tablespoons kosher salt to a boil. Cook cascatelli for 11 minutes. Reserve 1 cup of pasta water and drain.

Step 5

Transfer pasta to deep sauté pan or braising pan. Turn heat to medium. Toss pasta with mushrooms. Stir in 1/2 cup pasta water and crème fraîche. Cook for 1 to 2 minutes. If you want more sauce, add more pasta water. If you want your sauce thicker, raise heat briefly to reduce. Stir in oyster and king trumpet mushrooms. Stir in cheese and most of the parsley. Transfer to plates and garnish with the rest of the parsley. Serve with additional cheese and good-quality olive oil for drizzling.