Heat the olive oil in a large, heavy-bottom pot (at least 8 quarts) over medium heat.
Add the onions and carrots. Cook for 3 minutes, stirring frequently.
Add the garlic, 1 teaspoon salt, oregano, cumin, and black pepper. Cook for 1 minute, stirring often.
Add the ham shank, flank steak, pork stew meat, and the remaining 1 teaspoon of salt. Stir well.
Cook for 2–3 minutes to lightly brown the meat, stirring frequently.
Add the drained tomatoes and stir to combine.
Pour in 12 cups of water. Raise the heat to high and bring to a boil.
Once boiling, lower the heat to medium-low, cover the pot, and simmer for 60 minutes. Stir occasionally.
While the soup simmers, prep the vegetables in two batches:
Batch One: Peel and cut the green plantain, malanga, and yuca. Place them together in a bowl.
Batch Two: Prep the corn, boniato, pumpkin, and platano pinton (semi-ripe plantain). Keep the boniato in cold water to prevent browning.
After 1 hour, remove the ham shank from the pot. Set it aside to cool.
Add the green plantain, malanga, and yuca to the soup. Raise the heat to high and bring to a boil.
Lower the heat to medium-low, cover the pot, and simmer for 30 minutes, stirring occasionally.
Meanwhile, once the ham shank is cool enough to handle, remove the fat and bones, chop the meat, and return it to the pot.
Add the corn, boniato, pumpkin, and platano pinton. Raise the heat to high and bring to a boil again.
Lower the heat to medium-low, cover, and cook for 30 more minutes, or until all the vegetables are fork-tender.
Taste the ajiaco and add salt if needed. As a reference, we added 1½ teaspoons to ours.
Enjoy it on its own, or serve with a side of crusty bread for dipping or a side of white rice.