How to Make It
In a large pot of boiling salted water, cook the pappardelle until al dente; drain well.
Meanwhile, in a large skillet, heat 2 tablespoons of the olive oil. Add the shallot and a pinch of salt and cook over moderately high heat until the shallot is softened and golden, about 2 minutes. Add the mushrooms, season with salt and pepper and cook until the mushrooms are softened and most of their liquid has evaporated, about 12 minutes. Stir in the thyme. Scrape the mushrooms into a bowl and reserve.
In the same skillet, heat the remaining 2 tablespoons of olive oil. Season the chicken livers with salt and pepper and dredge them in flour, shaking off any excess. Fry the livers over moderately high heat, turning once, until browned and crisp, about 3 minutes per side.
Return the mushrooms to the skillet and pour in the Marsala. Cook for 1 minute, scraping up any browned bits from the bottom of the pan. Add 3/4 cup of the cream to the skillet at a time, allowing the sauce to thicken between additions. Simmer until the sauce coats the back of a spoon, about 3 minutes. Add the pappardelle and toss to coat. Transfer to a large bowl, garnish with the parsley and serve immediately.