Heat the oil in a large pot over medium heat. Cook and stir the green bell peppers, onion, and garlic in the hot oil until soft, 5 to 7 minutes. Add the sirloin roast to the pepper mixture and continue cooking until the beef is completely browned, 25 to 30 minutes.
Stir the chili beans, diced tomatoes, tomato sauce, water, chili powder, cumin, nutmeg, salt, black pepper, lime juice, and Worcestershire sauce into the pot; reduce heat to medium-low and cook 3 to 5 hours. Remove from heat and allow to cool slightly before chilling in refrigerator overnight.
Before serving, return pot to stove over medium-low heat; cook another 3 to 4 hours.