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.
Recipe courtesy Ana Sofia Pelaez