Build a low fire. Rake a bed of hot coals to one side of the fire pit and set a grate or tripod over them. For a 12-inch Dutch oven, a full baking heat is about 24 coals; chili wants a gentler fire, so use a single layer of coals under the pot and a few on the lid.
Soften the vegetables and bloom the spices. Heat the oil in the Dutch oven over the coals. Add the onions, bell pepper, chili powder, cumin, cayenne, and half the salt. Cook 5 minutes, stirring, until the onion softens and the spices smell toasted, not raw. Stir in the garlic and cook 30 seconds more.
Brown the beef. Add the ground beef and cook 10 minutes, breaking it up with a spoon, until no pink remains. Spoon off excess fat if the pot is swimming in it.
Add everything else. Stir in the beans, diced tomatoes with their juice, tomato puree, beef broth, and the remaining salt. Scrape the browned bits off the bottom of the pot as you stir.
Simmer covered. Put the lid on and let the chili simmer gently over low coals for 45 minutes, stirring once or twice so nothing catches on the bottom.
Simmer uncovered. Take the lid off and simmer 15 minutes more, until the chili thickens and clings to the spoon.
Rest and serve. Pull the pot off the coals and let it rest 10 minutes. Taste and add salt if it needs it. Serve with cheddar, sour cream, and green onions.