Soak chickpeas in water with a pinch of baking soda overnight, 10 to 12 hours. Drain and rinse well.
In a large heavy pot, combine chickpeas with 7 cups of water. Bring to a boil then lower heat to medium, cover, and simmer until just tender, 30 to 35 minutes. Drain and reserve 4 cups of the cooking water.
To make the sofrito, heat the oil in a large skillet over medium heat. Add the cubed ham and saute until lightly browned, 2 to 3 minutes. Add the onions, peppers and garlic and saute until soft, about 5 minutes. Add the tomatoes, wine, paprika and bay leaf to the sofrito, roughly crushing the tomatoes. Return to a simmer and cook an additional 5 minutes.
Return chickpeas to large pot with 4 cups of the reserved cooking water. Add the sofrito mixture to the chickpeas and bring to a simmer. Add the malanga and calabaza, and cook covered until the vegetables are tender, 35 to 45 minutes. Serve on its own with bread or over rice.