Bring a large pot of salted water to a boil. Add the pasta and cook according to the package instructions, about 8 minutes. Drain and set aside.
Season the chicken with 1 teaspoon salt and some pepper. Dredge in the flour and shake off the excess. Heat the oil and butter in a large saucepan over medium-high heat until the butter melts. Carefully place the dredged chicken into pan. Add the grated garlic. Cook until the chicken is golden brown and cooked through, 4 to 6 minutes. Transfer to a plate and set aside.
Pour the cream into the same pan and bring to a simmer. Stir in the Parmesan. Add the pasta to the mixture and toss to combine. Add the cooked chicken and gently toss. Garnish with the parsley and serve immediately.
Recipe courtesy of Trisha Yearwood