Cook pasta to near al dente in a large pot. Make sure that it is NOT done. It will finish cooking in the sauce. Drain and set aside.
Shave the Andouille in a food processor or chop into snall pieces. Heat skillet to medium-high and add 2 tbsp. oil. Cook andouille until it begins to brown and remove from skillet with a slotted spoon, leaving the oil and fat in the skillet.
Cut chicken breasts into bite-sized chunks and season with Cajun seasoning. Cook chicken in skillet until done. Remove with slotted spoon.
Slice onions and bell peppers into 1 inch strips and chop mushrooms. Sauté onions and bell peppers until the peppers are just slightly wilting. Add mushrooms and garlic cook for 2 more minutes.
Add chicken stock and scrape the pan. Let simmer for 2-3 minutes.
Add diced tomatoes and green chilies, thyme, and basil. Allow to cook down and combine for about 2 minutes.
Add heavy cream and allow to cook down for 2 more minutes.
Add meats and mixture in skillet to pasta in large pot and cook over medium heat until pasta is done and liquid is mostly absorbed. Do not overcook pasta.