Peel and devein shrimp, if desired. Combine shrimp and Creole seasoning in a medium bowl; set aside.
Cook bacon drippings, flour, and oil in a large skillet over medium heat, whisking constantly, 20 to 25 minutes or until roux is the dark brown color of pecan shells. Add 1/3 cup onion and next 3 ingredients; cook 5 minutes or until tender. Add thyme and next 3 ingredients; cook 1 minute, stirring constantly. Add shrimp and 4 green onions; cook over medium-high heat 3 minutes or until shrimp are almost done; transfer to a large bowl.
Add broth to skillet, scraping bottom of skillet to loosen browned bits. Add whipping cream. Bring to a boil over medium-high heat; reduce heat, and simmer 6 minutes. Add to shrimp. Stir in cooked pasta; toss well to combine. Pour into a lightly greased 13" x 9" baking dish. Sprinkle with Parmesan cheese.
Bake, uncovered, at 350° for 20 minutes or until thoroughly heated. Garnish, if desired.