Carefully thinly slice the chicken breasts in half widthwise. Season the slices generously with coarse salt and freshly cracked pepper on both sides.
In a rondeau or large pot, add 2 tablespoons of olive oil and heat over high heat until it lightly smokes. This is when you want to add the chicken. Place the slices in the pan and cook for about 4 to 5 minutes. You’re aiming for a beautiful golden-brown color.
Once the first side is browned, flip the chicken over and reduce to medium heat. Cook for another 4 to 5 minutes or until the chicken is cooked throughout. You can tell they’re done when they’re no longer pink in the middle. Once cooked, set the chicken aside on a cutting board to rest.
In the same pan, add 2 minced garlic cloves and 1 diced shallot with the remaining 1 tablespoon of olive oil. Sauté for about 30 to 45 seconds, just until fragrant. Be careful not to burn the garlic!
Pour in the heavy whipping cream and cook over medium heat for just 2 to 3 minutes to heat it up. This step is crucial because you want the cream to thicken slightly.
Next, stir in the grated parmigiano Reggiano. Lower the heat and let it melt slowly into the sauce, stirring continuously. This takes about 3 to 4 minutes, and you’ll notice the sauce becoming thick and creamy. Season with additional salt and pepper to taste.
While the sauce is simmering, bring a large pot of salted water to a boil. Add the fettuccine and cook according to the package directions, stirring occasionally. Aim for al dente, where the pasta still has a slight bite.
Once the pasta is cooked, reserve 1 to 1 ½ cups of the pasta cooking water. Drain the pasta in a colander, but don’t rinse it! The starch from the pasta helps the sauce stick.
Add the drained pasta to the pan with the Alfredo sauce. Toss it all together until the pasta is well coated. If the sauce seems too thick, add a ladle of reserved pasta water gradually until you reach your desired consistency.
To serve, slice the rested chicken into strips and lay it over the pasta. Sprinkle with additional parmigiano Reggiano and freshly cracked pepper if desired. Enjoy your delicious homemade Chicken Alfredo!