Heat oil in skillet over medium heat. Add chicken and season with salt and pepper. Cook 5-6 minutes per side, or until cooked through. Remove from heat.
Meanwhile, cook pasta according to package directions. Add broccoli florets during last 2 minutes of cooking. Drain and set aside. Slice once cooled.
Return skillet to heat. Add butter and garlic and cook 1-2 minutes, or until butter is melted. Sprinkle with flour, then slowly whisk in chicken stock until smooth. Whisk in milk and bring to a boil. Cook 1-2 minutes, or until sauce thickens. Add parmesan cheese and stir until cheese is melted and smooth. Season with salt and pepper, to taste.
Toss pasta, broccoli and sauce until mixed well. Top with chicken.