Cut roast into chunks, trimming away any excess fat. Season with Creole seasoning and set aside at room temperature for 30 minutes. Pour beef broth into a large saucepan and bring to a low simmer; reduce heat and keep warm.

Make the gravy: Heat ½ cup oil in a Dutch oven over medium heat; evenly sprinkle with flour and whisk until roux is the consistency of wet sand, adding more oil in small amounts if needed. Cook roux, stirring constantly with a flat-edged wooden spatula, 15-20 minutes or until the color of milk chocolate (do not burn). Gradually whisk in 6 cups heated beef broth in ½ cup increments,  vigorously whisking after each addition. Bring to a low boil, reduce heat to medium-low, and simmer 5 minutes, stirring constantly. Transfer gravy to a heat-proof container and set aside until needed.

Wipe Dutch oven clean and set over medium-high heat. Heat ½ cup vegetable oil in the Dutch oven over medium-high heat. In batches, evenly sear roast on all sides until nicely browned; set aside until needed.

If necessary, add a splash of water (or red wine if you have it) and scrape pan to loosen any browned bits. Add onion and sauté until onions are very soft, about 12 minutes. Add bell pepper, celery, and garlic; sauté until softened, about 5 minutes. Add tomato paste and sauté until caramelized and evenly distributed through pan, about 3 minutes. Deglaze with remaining 2 cups beef broth, scraping the bottom of the pan; bring to a simmer. Stir in reserved gravy and add seared meat in a single layer; add up to 1½ cups water so that meat is completely covered with liquid. Bring to a low simmer, cover, and adjust heat to maintain a low simmer. Cook, stirring occasionally, until meat is very soft and shreds easily, about 2 hours.

Remove from heat and gently remove beef to a large bowl; set aside to cool slightly. Let liquid remaining in pan sit undisturbed for 10 minutes or so; skim and discard any fat from the surface. Return to a low boil over medium heat. Simmer 10-20 minutes or until mixture is thickened slightly; taste and adjust seasonings. Shred meat and return to gravy; stir in green onions.