Cook the pasta in salted boiling water according to the package instructions. Add broccoli florets during the last 3 minutes of cooking. Drain and set aside.
Cut the chicken breast into bite-sized pieces and season with salt and black pepper.
Heat butter or olive oil in a pan and cook the chicken until golden brown and fully cooked.
Add minced garlic and cook for about 30 seconds until fragrant.
Pour in the cooking cream and stir in shredded cheddar cheese until melted and smooth.
Add the cooked pasta and broccoli to the sauce. Mix well until everything is coated with the creamy cheese sauce.
Serve hot with extra cheddar cheese and freshly ground black pepper.