Heat the oil in a Dutch oven or large, heavy-bottom pot over medium heat. Add the onion, green bell pepper, celery, and garlic. Cook, stirring frequently until the vegetables start to soften, about 5-7 minutes. Stir the tomato paste into the vegetables and cook for 2-3 minutes, stirring occasionally.

Add the water to the pot and stir well, scraping up any bits from the bottom of the pot. Add the ground beef. Use a wooden spoon to break the beef into small pieces. Add the tomato sauce, chili powder, cumin, cayenne pepper and kosher salt and black pepper then bring to a medium boil. Add the beans. Stir and reduce the heat to a simmer. Cook uncovered for 2-3 hours to reduce and thicken, stirring every so often.

Before serving, add the vinegar and taste for seasoning. Serve with shredded cheddar cheese, minced onion, and sliced jalapeño peppers. Refrigerate for up to 4 days or freeze for 4 months.