Heat oil in a 12-inch frying pan over medium high. Add onion, bell pepper and celery and cook, stirring occasionally, until vegetables are soft and just beginning to brown, about 6 to 7 minutes. Season with salt and pepper.
Add turkey or beef and cook, stirring occasionally and breaking up lumps with a wooden spoon or spatula, until meat is no longer pink, about 6 minutes. Add tomatoes, mustard, sugar, Worcestershire Sauce, catsup and hot sauce and bring to a simmer. Reduce heat and cook, stirring occasionally, until mixture is thickened and heated through, about 8 to 10 minutes. Taste meat mixture, adjust seasonings and season with salt and pepper; divide among buns and serve.