In a large saute pan, heat 2 tablespoons of the oil over a high flame. Add the turkey sausage and saute until golden brown, breaking up any large clumps, for about 5 minutes. Using a slotted spoon, transfer the sausage to a plate and set aside.
Heat 2 more tablespoons of oil in the same pan. Add the mushrooms and 1/2 teaspoon each of salt and pepper. Saute until all the liquid from the mushrooms has evaporated, about 8 minutes. Add the peas and saute for 2 minutes.
Return sausage to the pan and cook until the sausage is heated through and the flavors have blended, about 3 minutes.
Meanwhile, bring a large pot of salted water to a boil. Add the farfalle and cook, stirring occasionally, until al dente, about 8 minutes. Drain the pasta and reserve 1/2 cup of the cooking water.
Return pasta to pot and add the meat mixture. Toss over medium heat to combine and heat through, adding enough of the reserved cooking water to moisten, about 5 minutes.
Drizzle in the remaining oil. Season the pasta with more salt and pepper to taste. Remove the pan from the heat and add Parmesan cheese and toss to combine. Transfer pasta mixture to large bowl and serve.