Cook the pasta according to the package directions until al dente. Add the broccoli during the last 3 minutes of cooking. Drain and set aside.
Heat the olive oil in a large skillet over medium-high heat.
Add the chicken and season with the salt, black pepper, and Italian seasoning. Cook for 6 to 8 minutes until golden and cooked through. Transfer to a plate.
In the same skillet, melt the butter and add the garlic. Cook for 30 seconds until fragrant.
Stir in the flour and cook for 1 minute, stirring constantly.
Gradually whisk in the chicken broth, then stir in the heavy cream. Simmer for 3 to 4 minutes until slightly thickened.
Add the Parmesan cheese and stir until melted and smooth.
Return the cooked chicken to the skillet, then add the cooked pasta and broccoli. Toss until everything is well coated in the sauce.
Simmer for 1 to 2 minutes until heated through.
Garnish with fresh parsley and crushed red pepper flakes, if desired, before serving.