Start by bringing a large pot of salted water to a boil. Add the 12 ounces of fettuccine pasta and cook according to package instructions until al dente. Drain and set aside, reserving a bit of the pasta water for later.
While the pasta cooks, heat the 2 tablespoons of olive oil in a large skillet over medium heat. Season the 2 chicken breasts with 1 teaspoon of salt and 3/4 teaspoon of pepper. Once the oil is hot, add the chicken breasts to the skillet. Cook for about 6-7 minutes per side, or until the chicken is golden brown and cooked through. Use a meat thermometer to check that the internal temperature reaches 165°F. Remove from heat and let rest before slicing.
In the same skillet, lower the heat to medium-low and add the 3/4 cup of unsalted butter. Once melted, add the 4 cloves of finely chopped garlic and cook for about 1 minute until fragrant. Be careful not to burn the garlic!
Next, stir in the 2 tablespoons of all-purpose flour and whisk until smooth, cooking for about 1-2 minutes. Gradually add the 2 1/3 cups of heavy cream, whisking continuously to combine.
Once the heavy cream is heated through, stir in the 1 cup of grated Parmesan cheese, 1/2 teaspoon of salt, and 3/4 teaspoon of pepper. Stir until the cheese is melted and the sauce is smooth and creamy. If the sauce is too thick, add a bit of the reserved pasta water to reach desired consistency.
Add the drained fettuccine to the skillet with the Alfredo sauce. Toss to coat the pasta evenly with the sauce. If needed, adjust seasoning with more salt and pepper to taste.
Slice the cooked chicken breasts and place them on top of the fettuccine. Garnish with chopped fresh parsley and additional grated Parmesan cheese if desired. Serve immediately and enjoy the cheesy, creamy goodness!