Heat the olive oil in a large deep skillet or Dutch oven over medium-high heat. Season the chicken with salt, pepper, and Italian seasoning; cook 5 to 6 minutes until golden and cooked through. Remove to a plate.
In the same pot, add the onion and cook 3 minutes until soft. Add the garlic and cook 30 seconds until fragrant (don’t let it brown — bitter garlic ruins the whole pot).
Pour in the chicken broth and scrape up any browned bits — that’s pure flavor. Add the dry pasta, stir, and bring to a boil.
Reduce to a steady simmer, cover, and cook 11 to 13 minutes, stirring once halfway, until the pasta is tender and most of the liquid is absorbed.
Stir in the cream, Parmesan, and lemon zest. Return the chicken to the pot and fold in the spinach; cook 2 minutes until the spinach wilts and everything is creamy. Taste and add more salt if needed.