Season chicken generously with salt and pepper. Heat oil in a skillet over medium heat. Sear chicken until golden and cooked through, about 5–7 minutes per side. Remove and rest.
In the same pan, add garlic and sauté until fragrant, about 30 seconds. Don’t burn it—garlic should perfume, not scream.
Pour in heavy cream. Bring to a gentle simmer, then whisk in Parmesan until melted and smooth. If it thickens too much, splash a bit of pasta water.
Slice the rested chicken. Return it to the pan and coat with the creamy sauce. Add nutmeg if you’re using it and give a quick stir.
Meanwhile, cook pasta in salted water until al dente. Reserve a little pasta water, then drain.
Toss pasta with the sauce and chicken. If the sauce clings too thickly, loosen with a splash of pasta water. Finish with parsley.