"My mother-in-law, who is from Mexico, makes this and it's my husband's favorite. It's the Spanish version of meatballs, although it's cooked in a delicious broth instead of tomato sauce. Very filling... enjoy!"
Combine 1 cup chicken broth and tomato in a blender; blend until smooth.
Transfer tomato mixture to a large pot; add remaining 11 cups broth. Bring to a boil, skimming off any foam that rises to the top. Season broth with salt and pepper.
Mix ground chuck, hot pepper, garlic, and cumin together in a bowl. Season with salt and pepper. Scoop ground chuck mixture into a small ball; press 1 cube of pepper Jack cheese and 1 chunk of egg into the center and roll meatball to seal. Repeat with remaining chuck mixture, cheese, and eggs.
Lower meatballs gently into the boiling broth. Add potatoes, onion, white rice, and cilantro. Simmer until meatballs are no long pink and potatoes and rice are tender, 20 to 30 minutes.