Combine beef, flour, eggs, and 1/2 cup of the broth. Set aside.
In an 8-quart kettle bring remaining broth, consommé, oregano, onions and chile to boil, reduce heat to low.
Quickly shape meat mixture into balls about 1 1/2 inches in diam., and drop into stock. Simmer meatballs, uncovered for 5 minutes, then spoon off any fat and foam from surface.
Add carrots, rice and coriander. Simmer, uncovered, for 20 minutes or until carrots and rice are tender to bite.
Meanwhile, discard spinach stems; wash leaves well, then cut crosswise into thin shreds. Add spinach to stock and cook, uncovered, 5 minutes longer. Ladle into wide soup plates or bowls. Pass lime to squeeze over all.