In a large saute pan over high heat, add 2 tablespoons of olive oil. Season turkey with salt and pepper. Add turkey and saute breaking any large lumps until golden brown. Add two more tablespoons of olive oil and add chopped mushrooms. Season with salt and pepper. Saute until all the liquid from the mushrooms has evaporated, about 5 minutes. Add the peas and saute for 4 minutes. Turn off the heat.
2When water comes to a boil, add the farfalle. Cook until al dente. Drain in a colander (save some of the pasta water) or use a spider to remove pasta from the pot and add to the pan with the turkey mixture. Gently heat over medium heat for 5 minutes. Drizzle with remaining olive oil. Add some of the pasta water to the mixture to coat.
3Turn off the heat and add the grated cheese. Serve with additional cheese over top if you like.