Cut the chicken breast fillet into half-inch cubes.
Crush, peel and mince the garlic.
Melt the butter in a wide shallow pan.
Spread the chicken cubes in a single layer. Sprinkle with salt and pepper. Cook over medium heat for a minute without disturbing them.
Add the minced garlic to the chicken. Cook, stirring often, for another minute.
Add the broccoli florets to the chicken. Sprinkle in more salt and pepper. Cook the broccoli with the chicken, stirring often, for a minute. Scoop out the chicken and broccoli; transfer to a plate.
Set the heat to low. Pour the cream and milk into the pan. Add the cream cheese, breaking it into small pieces with a spatula. Cook the sauce, stirring a few times, just until simmering and the cream cheese is melted. Taste. Add salt and pepper, as needed.
Add the cooked pasta to the pan and toss to coat every noodle with the rich creamy sauce.
Turn off the heat. Add the chicken and broccoli to the noodles. Stir a few times.
Serve the chicken broccoli pasta with cream sauce immediately.