Boil pasta al dente (10-12 minutes), drain and place back in stock pot with one tbsp. of olive oil. Toss pasta with olive oil to keep from sticking. The pasta will cook some more when it is incorporated with the cream sauce.
While pasta is boiling, melt half a stick of butter and a tablespoon of olive oil in a large dutch oven over medium high heat.
Sauté onions for a few minutes and then add red pepper and mushrooms, after a few more minutes add the green onions and the garlic, stir all together and add the chicken stock.
Stir in the Creole seasoning, thyme, oregano, salt and black pepper. Allow chicken stock to boil and reduce, about 2 more minutes.
Add the crawfish tails and any liquid from their package and stir them into the mixture, allowing the fat and flavor from tail to incorporate with all the ingredients. Stir for another 2 minutes.
Remove crawfish tails from mixture as best as you can and reserve. It's OK if all some of the other ingredients stick to the crawfish tails. You just want to make sure that the tails do not over cook and become tough or rubbery.
Add the heavy cream, bring to a boil and reduce heat to a simmer. Reduce heavy cream until it is thick enough to coat your spoon, about 7 to 10 minutes (Be patient, this is the key step to success with this dish).
Incorporate the grated cheese and stir. Then add back in the crawfish tails and any bits that stuck to them back into the sauce.
Fold in the pasta and cook on low for 2 to 3 minutes. Sprinkle on the parsley and serve with hot French bread and a salad.