Heat a large heavy bottom skillet or pan over medium-high heat. While the pan is heating, generously salt the pounded chicken breasts on both sides. Add several tablespoons of a neutral cooking oil of your choice to the pan. Add the chicken and cook for approximately 15-minutes, flipping occasionally until golden brown on the outside and internal temperature reaches 165°F on an instant read thermometer. Remove from pan, and loosely tent with foil and rest while you make the sauce.
Alfredo Sauce
Bring a large pot of heavily salted water to a boil. Add pasta and cook according to package directions until al dente (about 10 - 12 minutes), then drain.
While the pasta is cooking, add garlic to the same pan you cooked the chicken in and sauté for 30-seconds until fragrant. Add the heavy cream and lemon juice and scape the bottom to deglaze. Reduce heat to medium-low to avoid curdling the heavy cream. Add the butter and melt, approximately 1 to 2-minutes. Once Add salt, pepper, lemon zest, parmesan cheese, and a small pinch of nutmeg stirring to incorporate evenly. Bring to a slight simmer and cook for 5 to 6 minutes minutes until the sauce has thickened slightly. While the sauce is simmering, slice the cooked chicken breasts.
Assembly
Once the pasta is done, transfer the cooked pasta to the pan with the sauce and add several splashes of pasta water. Toss to coat evenly. Place some pasta on a plate, and top with a portion of sliced chicken. Garnish with more parmesan, parsley, lemon zest, and serve.