Season the chicken with 1/4 teaspoon salt and 1/4 teaspoon pepper.
Heat the oil in a 12-inch skillet over medium-high heat. Add the chicken and cook, stirring, until the chicken is browned on both sides, and almost entirely cooked through. Remove the chicken from the skillet. Add the onions and cook for another 3 to 4 minutes, until softened. Add in the garlic and lemon zest and cook for another minute or two.
Pour 2 1/2 cups of the broth into the pan. Bring to a boil. Stir in the pasta and remaining 1/4 teaspoon of salt and pepper and reduce heat to medium. Cover and cook for 11 minutes. Uncover, add the broccoli, cooked chicken and remaining 1/2 cup of the broth. Cover and cook for 3 to 5 minutes, or until the pasta is al dente and the broccoli is crispy/tender.
Stir in the cream cheese, Parmesan and lemon juice until smooth. Cook for another 1 to 2 minutes, or until the sauce is creamy and coats the pasta. Remove from heat and let sit for a few minutes. It will continue to thicken as it sits. Serve hot, with extra Parmesan for sprinkling.