Heat the oil in a large aluminum pan, add the sugar, and let it melt and caramelize until it turns deep brown. Then sear the meat on all sides.
Add the squash and one whole plantain to the pan with the meat. Pour in 4 to 6 cups of water—just enough to cover everything—and add the bouillon cubes. Bring to a boil, then cover and simmer for 40 minutes.
While everything simmers, peel and slice the remaining plantains into ½-inch rounds. Then peel and cut the yuca, yautía, and batata into 1-inch pieces. Soak them in water to keep from browning. Tip: soak the batata separately
Once the squash and whole plantain are soft, remove them from the pot with a few tablespoons of the cooking liquid. Mash by hand until smooth (you can use a food processor for this step if you’d like).
Drain the root vegetables, then add them to the pot along with the mashed squash and plantain. Stir everything together, lay the cilantro on top, and cook for another 35-45 minutes, until the vegetables are tender.
Turn burner off, discard cilantro and add the fresh lime juice. Cover and let rest for 10-15 minutes.
Spoon into bowls and serve with white rice and sliced avocado on the side.