In a large Dutch oven over medium-high heat, heat the olive oil. Add the beef, sausage, onion, celery, bell pepper, and garlic.
Cook, stirring and breaking up the meat, until the beef and sausage are no longer pink. Drain off the excess grease.
Stir in the tomato sauce, diced tomatoes, tomatoes with green chilies, water or broth, black eyed peas, chili powder, Creole (or Cajun) seasoning, sugar, and salt. Mix well.
Bring to a boil, then reduce the heat to low. Cover and simmer for about 45 minutes to 1 hour, stirring occasionally. If you like a thicker pot of chili, simmer uncovered for part of the cooking time. Taste and add extra salt, sugar, a splash of broth, or some cayenne pepper if needed.
Ladle into bowls, garnish with optional toppings, and serve.