Boil the pasta: Bring a large pot of well-salted water to a boil. Cook pasta until just shy of al dente according to package directions.
Add the broccoli: During the last 2 minutes of pasta cook time, stir in the broccoli florets. Cook until bright green and crisp-tender. Reserve 1 cup pasta water, then drain.
Cook the chicken: While pasta boils, heat olive oil in a large skillet over medium-high heat. Add chicken, Italian seasoning, salt, and pepper. Sear, stirring occasionally, until cooked through and lightly golden, about 5–7 minutes. Transfer chicken to a plate.
Sauté the garlic: Reduce heat to medium. In the same skillet, add a quick splash of broth and the minced garlic. Cook 30–60 seconds until fragrant.
Build the sauce base: Whisk in remaining broth and milk. Stir in the light cream cheese until mostly melted.
Thicken it: In a small bowl, whisk cornstarch with 2 tablespoons water to make a slurry. Slowly whisk slurry into the pan. Simmer gently 1–2 minutes, stirring, until slightly thickened.
Add Parmesan off heat: Turn off the heat. Stir in Parmesan until melted and smooth. Add lemon juice and red pepper flakes if using. Taste and adjust salt and pepper.
Toss it all together: Add the cooked chicken, drained pasta, and broccoli to the skillet. Toss, loosening with reserved pasta water a splash at a time until the sauce clings silkily.
Finish and serve: Sprinkle with extra Parmesan and parsley. Serve hot.
