In a large saucepan, over medium heat, add the oil. Season the duck pieces with salt and pepper. Place the flour in a mixing bowl. Season the flour with salt and pepper. Dredge the duck pieces in the seasoned flour. When the oil is hot, add the duck pieces, fat side down and sear for 6 minutes. Turn the pieces over and continue to sear for 4 minutes. Remove the duck from the pan and set aside. Add the onions, carrots, and celery. Season the vegetables with salt and pepper. Saute the vegetables until wilted, about 4 minutes. Stir in the tomato paste. Deglaze the pan with the red wine. With a wooden spoon, scrape the sides and bottom of the pan to loosen any brown particles. Stir in the garlic, duck stock and water. Add the potatoes, reserved duck pieces, and thyme. Bring the liquid to a boil and reduce to a simmer. Simmer for about 3 hours, covered, stirring occasionally or until the meat falls off the bones. Remove from the heat and stir in the parsley. Ladle into shallow bowls and serve with crusty bread.