Bring a large pot of lightly-salted water to a rolling boil. Stir the rotini into the boiling water. Cook uncovered, stirring occasionally, until the pasta has cooked through, but is still firm to the bite, about 8 minutes. Drain well in a colander set in the sink.
Meanwhile, heat the olive oil in a large saucepan over medium heat. Stir in the tasso, and cook until golden brown, about 5 minutes. Stir in the garlic, onion, green pepper, green onion, and celery. Cook and stir until the onion has softened and turned translucent, about 5 minutes. Add the basil, thyme, Cajun seasoning, and hot sauce; cook 1 minute.
Pour in the cream, and bring to a simmer over medium-high heat. Reduce heat to medium-low and stir in the Parmesan cheese. Cook and stir until the sauce begins to thicken slightly, about 3 minutes. Add the shrimp and crawfish tails, and cook until hot, then toss with the rotini pasta. Sprinkle with parsley to serve.