Cook pasta according to package instructions. Drain and set aside.
Steam broccoli until tender-crisp, about 4-5 minutes.
Heat olive oil in a large skillet over medium heat. Add chicken slices, season with salt and pepper, and cook until golden and cooked through, about 6-7 minutes. Remove chicken and set aside.
In the same skillet, add minced garlic and cook until fragrant, about 1 minute.
Sprinkle flour over garlic and stir to form a roux, cooking for 1-2 minutes.
Gradually whisk in low-fat milk, stirring constantly until sauce thickens, about 3-5 minutes.
Stir in Parmesan cheese until melted and smooth. Adjust seasoning with salt and pepper.
Add cooked chicken, broccoli, and pasta to the sauce. Toss gently to combine and heat through.
Garnish with fresh parsley if desired and serve immediately.