In a large pot, cook the chorizo over medium-high heat, stirring, until the fat is rendered. Add the onions and garlic and cook, stirring, until soft, about 4 minutes. Stir in the salt and pepper, and add the pork ribs, beef shoulder, beef ribs, beef shanks, bay leaves, cilantro and parsley stems. Add enough water to cover by several inches, about 1 gallon, and bring to a boil. Lower the heat and simmer uncovered, stirring occasionally and skimming the top to remove any foam that rises to the surface. Cook until the meat is tender, adding more liquid if needed, about 1 1/2 hours.

Add the cabbage, corn, potatoes, sweet potatoes, and carrots. Cook, stirring occasionally, until the vegetable are tender, about 20 minutes. Adjust the seasoning, to taste.

Remove the meat with a mesh strainer and arrange on a platter. Garnish with the chopped green onions.

Discard the bay leaves from the broth and ladle into large soup bowls or a tureen. Garnish each serving with chopped cilantro and parsley. Serve hot.