Add the butter and olive oil to a fairly large pot over medium-high heat.
Add the onion to the pot and sauté for about five minutes, stirring occasionally (ok if it lightly browns).
Meanwhile, cut the chicken breasts into bite-size strips, and trim off any excess fat/gristle if necessary. Add chicken to the pot and cook it for a couple of minutes until the outside of the chicken turns white.
Add the sun-dried tomatoes, chicken broth, cream, water, Cajun seasoning, garlic, and pasta to the pot. Stir. Increase heat to high. Once it comes to a boil, reduce heat to medium-high (or lower) so it's gently boiling.
Cook for 10-15 minutes (stir occasionally so pasta won't stick to the bottom) or until the pasta is done and the liquid is reduced to a level you're satisfied with.
Stir in the parmesan cheese and basil before serving.