Pound the chicken breasts to equal thickness. Place the chicken breasts between 2 sheets of plastic wrap on a cutting board. Pound the thick side of each chicken breast with a meat mallet until it is about as thick as the thin side. Note: Skip this step if you're baking the chicken in the oven.
Season. Remove the chicken from the plastic and pat it dry with paper towels—season with Italian seasoning, ½ teaspoon of salt, ½ teaspoon of black pepper, and paprika.
Heat the oil and butter and add the chicken. Melt 2 tablespoons of butter with 2 tablespoons of olive oil in a large skillet set over medium-high heat. After the butter has melted, swirl the pan to redistribute the oil. Add the chicken and let it cook for 5-6 minutes, undisturbed, until the bottom is golden brown.
Cook the chicken to 160℉. Flip the chicken and continue to cook until it reaches an internal temperature of 160-165℉ as measured by a digital thermometer. Once the chicken is fully cooked, remove to a clean cutting board, cover with foil, and let it rest until serving. Cook the pasta, reserve the cooking water, and drain. In the meantime, bring a large pot of (generously salted) water to a boil. Once it reaches a rolling boil, add the pasta and cook until al dente, about 8-10 minutes. Reserve 1-2 cups of the pasta cooking water, then drain the pasta.
Melt the remaining butter and add the garlic. In the same skillet, melt the rest of the butter over medium heat. Once melted, stir in the garlic and cook until fragrant, about 1 minute.Optional: For a little extra flavor, deglaze the skillet with a splash of dry white wine before adding the garlic. Make a roux (optional). If you prefer a thicker Alfredo sauce, whisk 1-2 tablespoons of flour (max!), ½ teaspoon of salt, ½ teaspoon of black pepper, into the butter. Whisk continuously until it turns a light golden color.
Add the heavy cream. Stirring continuously, slowly add the heavy cream. Simmer gently over low heat for 3-4 minutes.
Add the Parmesan cheese. Stir in the freshly grated parmesan cheese. Whisk continuously until the cheese has melted into the sauce. If the sauce is too thick, add some of the reserved pasta cooking water, a few tablespoons at a time.
Add the drained pasta. Add the drained fettuccine pasta and toss to coat in the sauce. Season with additional salt and black pepper, to taste.
Slice the chicken, garnish, and serve. Slice the chicken into thin strips and serve it directly over the pasta or divided among serving bowls. Garnish with fresh chopped parsley, additional Parmesan, a splash of lemon juice, and black pepper, if dresired.