Bring a large pot of heavily salted water to a boil.
Toss the chicken in a bowl with olive oil, lemon zest, and spices until thoroughly coated. Heat a large high-sided skillet over medium heat and cook the chicken for 7 to 10 minutes until golden and the internal temperature reaches 165°F. Transfer to a plate and cover to keep warm.
Cook the pasta until just shy of al dente, reserving 1 cup of cooking water before draining. In the same skillet, sauté the onion in butter over medium heat for 4 to 5 minutes until soft, then add garlic and cook until fragrant. Stir in the heavy cream, broth, salt, and pepper, then simmer uncovered for 5 to 6 minutes until thickened before mixing in the parsley, Parmesan, lemon zest, and juice.
Add the pasta and 1/2 cup of reserved water to the sauce, tossing vigorously over medium-high heat for 2 minutes until glossy. Incorporate more pasta water if the sauce is too thick, then remove from heat once the sauce is thickened and glossy.
Thinly slice the chicken and arrange it over the pasta. Garnish with fresh parsley, Parmesan, black pepper, and a squeeze of lemon juice.
