Heat the olive oil in a large pot over medium heat; fry the plantains and potatoes in the hot oil until crisp on the outside, 5 to 7 minutes. Remove from the pot and set aside, keeping the oil in the pot.Advertisement
Cook and stir the onion and garlic in the hot oil until the onion is translucent, 5 to 7 minutes. Add the chicken and chorizo; season with salt and pepper. Cover the pot and cook for 5 minutes.
Pour enough water over the chicken to cover completely; bring to a simmer and cook for 10 minutes. Add the tomatoes, cover, and cook another 10 minutes. Stir the plantains, potatoes, garbanzo beans, and cabbage into the mixture. Cook covered until the cabbage is wilted and everything is hot, about 5 minutes more. Serve hot.