Heat olive oil in a large, covered cooking pot over medium-high heat. Season chicken with salt and pepper. Cook and stir chicken in hot oil until browned, 5 to 7 minutes.

Add sausage to chicken in the pot and continue cooking until sausage is lightly browned, about 5 minutes more. Stir in garlic and cook for about 2 minutes. Add chicken broth, heavy cream, pasta, and Cajun seasoning. Stir together and bring to a simmer over medium-high heat, about 5 minutes.

Reduce heat to low, cover the pot, and cook until pasta is tender, 15 to 20 minutes.

Remove the pot from heat and stir in Parmesan cheese. Stir in parsley and sprinkle with additional Cajun seasoning.