In a large Dutch oven, heat the oil. Brown the chicken and set aside.
Preheat oven to 375 degrees F.
In the same pan add more oil, if necessary, and add the peppers, onions, and garlic. Cook until the vegetables start to soften and caramelize, about 5 minutes. Add the ground cumin, coriander, and cayenne. Cook for another 5 minutes. Remove the pepper mixture and puree until smooth in a food processor and set aside.
In the same pan, add the chicken back in, along with the malanga, green plantain, and calabaza. Pour in the chicken stock and the pureed pepper mixture (sofrito). Cover and cook in the oven until the chicken is falling off the bone and the vegetables are tender, about 1 hour.
Serve garnished with chopped cilantro.