Heat 1 tablespoon of the olive oil in a 12-quart pot over medium-high heat. Season the chicken pieces with salt then, working in batches, brown them on all sides. Transfer the chicken to a platter and set aside.
Add the ¼ cup of olive oil to the same pot, and when the oil is hot, add the onions and peppers. Reduce the heat to low and cook slowly until the vegetables are dark golden brown, about 30 minutes. Add 1 tablespoon of water if the onions start to burn. Add the garlic and cook for 5 more minutes. Then add the white wine and cook until it evaporates, 4 to 5 minutes.
Add the jamón and browned chicken pieces, as well as any juices that have collected, and cook for 5 more minutes. Stir in the pimentón, tomato sauce, rosemary, bay leaf and the water and simmer over low heat for 1 hour or until the meat starts to fall off the bone. Season to taste with salt before serving.