
In a large skillet over medium-high heat, heat oil. Add chicken and season with salt and pepper. Cook until golden and cooked through, 8 minutes per side. Let rest 10 minutes, then slice. Add milk, broth, and garlic to skillet. Season with salt and pepper and bring to a simmer. Add fettuccine, stirring frequently for about 3 minutes. Let cook until al dente, 8 minutes more. Stir in heavy cream and Parmesan until combined. Simmer until sauce thickens. Remove from heat and stir in sliced chicken. Garnish with parsley.