Sauté the beef, onions, and garlic in a large kettle or stockpot over medium heat until the meat is no longer pink. Break up any large clumps of meat with a spoon.
Add the tomato paste, Worcestershire sauce, vinegar, chili powder, paprika, cinnamon, black pepper, cayenne, cumin, allspice, cloves, bay leaf, and salt along with 3 cups of water and bring to a boil.
Reduce the heat and simmer the chili for an hour. Taste and adjust the seasonings and continue to simmer for an additional hour, adding more water if necessary.
The chili should be thick but still be able to be ladled over the spaghetti. Discard the bay leaf before serving.
Put the accompaniments into serving bowls. To serve, place in the spaghetti into bowls, ladle the chili over the top and allow your guests to garnish the 2-Way chili with whatever accompaniments they choose. Serve the crackers on the side.