Slice and Season Chicken: Place each chicken breast flat on a cutting board and slice it horizontally through the center to create two even cutlets of equal thickness. Pat all four cutlets completely dry with paper towels, removing as much surface moisture as possible. Season both sides of each cutlet evenly with 1 teaspoon of kosher salt and 0.5 teaspoon of black pepper. Dry, well-seasoned chicken forms a proper sear in the skillet rather than steaming against the pan surface.
Boil Salted Pasta Water: Fill a large pot with 4 liters / 1 gallon of water and bring it to a full rolling boil over high heat, approximately 12 minutes. Add 1 tablespoon of kosher salt directly to the boiling water. Heavily salted water seasons the fettuccine from within the pasta strand rather than only at the surface after plating.
Sear the Chicken Cutlets: Heat 2 tablespoons of olive oil in a 12-inch stainless steel skillet over medium-high heat for 2 minutes until the oil shimmers and a drop of water evaporates immediately on contact. Place two cutlets flat in the skillet and cook for 4 minutes without pressing or moving them until the undersides develop a deep golden crust that releases cleanly from the pan. Flip each cutlet with tongs and cook the second side for 3 minutes until the internal temperature reads 74°C / 165°F on an instant-read thermometer inserted into the thickest point. Transfer the cooked cutlets to a clean cutting board and repeat with the remaining two cutlets. Rest all four cutlets for 5 minutes before slicing.
Cook the Fettuccine: Add the dry fettuccine to the boiling salted water and cook for 9 minutes, stirring once at the 3-minute mark to prevent the strands from clumping together, until the pasta is al dente with a slight resistance at its center when bitten. Before draining, ladle 120ml / 0.5 cup of the starchy pasta cooking water into a heatproof measuring cup and set it aside. Drain the fettuccine through a colander and do not rinse it, as the surface starch helps the Alfredo sauce adhere to each strand.
Build the Alfredo Sauce: Reduce the heat under the same skillet used for searing to medium and add 2 tablespoons of unsalted butter. Once the butter melts completely and begins to foam, add the minced garlic and cook for 1 minute, stirring constantly with a wooden spoon, until the garlic is fragrant and pale gold. Pour in 240ml / 1 cup of heavy cream and stir it into the butter and garlic mixture. Cook the cream for 4 minutes, stirring every 30 seconds, until it reduces slightly and coats the back of the wooden spoon in a thin, even layer.
Finish with Cheese and Pasta: Remove the skillet from the heat completely before adding the Parmesan. Add the 100g / 3.5oz of grated Parmigiano-Reggiano in two batches, stirring each addition in a circular motion until the cheese melts fully into the cream and no visible shreds remain. Add the 0.25 teaspoon of nutmeg and stir to incorporate. Add the drained fettuccine directly to the skillet and toss the pasta through the sauce using tongs for 1 minute, adding the reserved pasta water 2 tablespoons at a time until the sauce reaches a smooth, glossy consistency that clings to every strand. The sauce should coat the pasta without pooling at the bottom of the pan.
Slice Chicken and Plate: Slice the rested chicken cutlets on the cutting board into strips approximately 1.5cm / 0.6in wide, cutting against the grain of the muscle fibers. Divide the fettuccine Alfredo evenly among four wide, shallow bowls using tongs. Arrange the sliced chicken strips over the top of each portion. Garnish each bowl with a pinch of chopped flat-leaf parsley and a light dusting of additional grated Parmesan. Serve immediately while the sauce remains fluid and the pasta is at full temperature.
