Cut off and set aside turkey wing tips and cut the wings in half at the joint. In a large, heavy pot, heat the oil over moderately high heat, add the wings including the tips, and brown lightly on all sides. Add the onions, carrots, and garlic and cook, stirring, until the onions are soft. Add the tomatoes and stir for 1 minute. Add the bay leaves, tarragon, salt and pepper, and water and bring to a boil. Reduce the heat to moderately low, cover, and simmer until the wings are tender, about 2 hours.
Discard the wing tips and bay leaves, transfer the wings to a bowl, remove and discard the skin and bones, and cut the turkey meat into 1 1/2-inch strips. Pour off all but about 2 cups of the steaming liquid, add the turkey strips, ham, and peas to the pot, return the stew to a simmer, and cook until the peas are tender, about 10 minutes. Add the rice and stir until well blended.