Bring a large pot of salted water (about 4 quarts with 1 Tbsp salt) to a boil. Add the fettuccine and cook according to the package directions until al dente. Drain and set aside.
While the pasta cooks, slice your chicken into strips. Season them with salt and pepper. In a large skillet over medium-high, heat 2 Tbsp olive oil and sauté the chicken until it turns lightly golden and is cooked through (about 5 minutes). Move the chicken aside and keep it warm.
In that same skillet, heat the remaining 1 Tbsp olive oil plus butter over medium-high. Add the chopped onion and sauté three minutes until soft. Add the sliced mushrooms and cook 5–7 minutes until they’ve softened, then stir in the minced garlic for 30 seconds or until fragrant.
Pour in the half and half and let it simmer over medium-high for 8–10 minutes, until it just begins to thicken. Return the chicken to the pan, stir in ¼ cup parsley, and season with salt and pepper to your taste.
Add the cooked pasta into the sauce and toss to coat. Heat for another minute until everything is warmed through. Turn off the heat and cover. Let the dish rest for 10–15 minutes so the sauce sets a bit. Stir before serving and garnish with extra parsley.