Cook pasta according to package directions; drain. Set aside. For quicker cooking, pound chicken breasts until thin and even. Slice each breast into thirds. Place chicken pieces in a zip-top bag. Add ¹/³ cup flour, salt and pepper to bag. Shake to coat chicken with flour. Heat oil in a large nonstick skillet over medium-high heat. Add chicken to hot oil and cook for 3 to 4 minutes per side or until browned and done. Remove chicken to a plate. Add broccoli, onion and garlic to skillet. Cook for 2 to 3 minutes, stirring frequently. Add ¾ cup chicken broth. Return chicken to skillet and reduce heat to a simmer. Simmer for 3 to 4 minutes. In a small bowl, combine remaining 1 cup chicken broth, milk and remaining ¼ cup flour; whisk until blended. Add ¼ cup cheese. Pour into skillet and bring to a simmer, stirring constantly. Simmer for 3 to 4 minutes or until thick, stirring gently and frequently. Serve chicken and broccoli in sauce over fusilli pasta. Sprinkle with additional Parmesan, if desired.