Prepare pasta in salted water according to package directions. Drain and set aside.
While pasta is cooking prep the chicken, peppers, and onion.
In a small drinking glass mix together the cornstarch and water.
In a large, lightly oiled skillet, over medium high heat, season the chicken with salt, pepper and Cajun seasoning to taste. Cook the chicken until lightly browned and juices run clear. Remove from the skillet and set aside. Remove any excess oil from the skillet.
Using the same skillet melt the butter over medium heat, add the olive oil, mushrooms, peppers, and onion. Stir in the seasoning and cook until vegetables are tender. Stir in the “half and half,” and cream. Bring to a simmer, mix in the water and cornstarch mixture, stir and cook until thickened.
Combine the sauce, chicken, and pasta together and cook until chicken is heated through.