Add the turkey fat to a large pot over medium-high heat. Add the shallots and saute until translucent. Whisk in the flour and cook until medium golden brown in color, about 3 to 4 minutes. Slowly whisk in pan the drippings with the stock and bring to a boil, then reduce the heat. Simmer until thick or until desired consistency is reached, about 10 to 15 minutes. Stir in the chopped egg and season with salt and pepper, to taste, if needed. Serve alongside that big beautiful bird!