Cook pasta al dente according to package directions. Add the broccoli florets to the pasta during the last minute of cooking. Turn off heat and drain pasta.
While the pasta is cooking, Heat a large pan on medium heat. Add the olive oil to pan. Season chicken breasts with salt and pepper and add to the pan. Cook chicken breasts for 5-6 minutes per side or until cooked through. Remove from pan, cool for 5 minutes then slice or dice.
To the same pan, add the minced garlic and 1 tablespoon olive or butter. Sautee for 30 seconds to 1 minute or until light golden, be careful not to burn garlic. Whisk in flour until lightly browned, about 1 minute. Gradually whisk in chicken stock and milk, whisking constantly, until incorporated. Bring the mixture to a simmer. Turn off heat and stir in Parmesan cheese, salt and pepper.
Add cooked drained pasta and broccoli to the sauce. Top with cooked (diced or sliced) chicken breasts. Toss to combine or serve chicken on top. Top with more parmesan cheese or parsley, if desired. Enjoy!