Add the oil to a large pot (or large high sided skillet). Place over medium-high heat for two minutes. Add the chicken and the Cajun seasoning. Cook for 5 minutes, stirring occasionally. Add the garlic. Cook 1 minute, stirring often.
Add the broth and milk. Break the pasta in half and add it to the pot. Cover and bring to a rapid, rolling boil, stirring occasionally. *Note: Watch the pot carefully during the beginning of the cooking process as milk tends to boil over easily.
Reduce the heat to medium-low and let the pasta simmer, covered, for 8-13 minutes. Stir every 2-3 minutes to prevent sticking. Cook until there is ¼ to ½ inch of liquid in the bottom of the pot.
Remove the pot from the heat. Stir in the parmesan cheese. Serve immediately.
