Add the olive oil to a large Dutch oven and heat over medium heat until hot. Season the turkey with the salt and pepper. Add half of the turkey legs to the pan and cook until well browned on both sides, about 3 to 4 minutes per side. Set the seared turkey legs on a platter once browned and repeat with the remaining turkey legs. Once all the turkey legs are browned, add the onions, carrots and celery to the pan. Saute the vegetables until softened, about 3 to 4 minutes.
Add the leeks, garlic, green onions and ginger to the pan and saute for 1 minute, stirring often. Add the tomato paste and stir well to incorporate. Sprinkle the flour over the vegetables and stir to combine. Cook, stirring for 3 minutes. Add the Guinness to the Dutch oven and increase the heat to medium-high. Bring the Guinness to a boil and cook for 5 minutes. Add the stock and allspice, stir, and return the turkey legs to the pan. Return the pan to a boil and reduce to a simmer. Cover and continue to cook the turkey legs until tender, about 2 to 2 1/2 hours. Remove the lid, and stir the chopped parsley into the pan. Serve immediately over steamed white rice.