1Pat the chicken dry, pound to an even thickness, coat with 1 tbsp olive oil, and season both sides.
2Boil the pasta in salted water until just shy of al dente; save at least 1/2 cup pasta water before draining.
3Heat a large pan or pot over medium heat, add 2 tbsp olive oil, increase to medium-high, and sear chicken for 3–4 minutes per side until golden and cooked through.
4Melt the butter in the same pan, scraping up fond; add shallot and cook for 5 minutes, then add garlic and cook for 1 minute.
5Reduce heat to medium-low, slowly pour in the cream, add seasonings, and simmer for 2–3 minutes.
6Reduce heat to low, add parmesan, and stir until smooth.
7Add pasta and 1/4 cup pasta water, toss over low heat for 1–2 minutes until silky; add more pasta water as needed, slice the chicken, and top with more parmesan and fresh parsley.