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

Add sausage to the pot and continue to cook until 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 chopped parsley and sprinkle with additional Cajun seasoning if desired.