Cut the fresh and smoked ham into large pieces about 3 inches by 3 inches and set aside.
In a large stockpot, saute the carrots and onions. Add 3 tablespoons of tomato paste and carmelize the mixture. Add the pieces of fresh and smoked ham. Add enough water to cover (approximately 1 gallon). Add the bay leaves and white wine and then bring to a boil and cook until very tender, about 1 1/2 hours, adding more water as needed. Strain and reserve the liquid.
Shred the meat and set aside.
In a medium size skillet, saute the julienne tomato and onion. Add the garlic cloves. Crush the canned tomatoes by hand and add to the mixture. Add the sun-dried tomatoes. Add the Sherry vinegar and cook for 5 minutes. Add the shredded ham and slow cook for 15 minutes (add the reserved cooking liquid from the ham to keep stew moist at all times). Season with salt and pepper and serve with yellow rice.