For the sauce: Place a large sauté pan or rondeau over medium-high heat. Add the olive oil and duck bones and necks and deeply brown on both sides. Add the onions, carrots, celery, lemongrass, garlic, bay leaves, thyme and a large pinch of salt and stir. Add the wine and stock and simmer for at least 1 hour, allowing the flavors to meld.
Meanwhile, place a medium saucepan over medium heat, add the sugar and vinegar and bring to a simmer, whisking to dissolve the sugar. Add the orange juice and continue to simmer the gastrique until syrupy, 8 to 10 minutes. You should have around 1/2 cup.
When the stock mixture is ready, strain it and add 1/2 cup to the gastrique, whisking to combine. Simmer until reduced by half, 10 to 15 minutes, then keep the sauce warm.
For the duck: While the sauce is reducing, score the skin on the duck breasts in a crosshatch pattern using a very sharp knife and being careful not to cut into the meat. Season the breasts on both sides with salt and pepper and place skin-side down in a cold large sauté pan coated with a drizzle of olive oil.
Place the pan over medium-low heat and slowly render most of the duck fat, 8 to 10 minutes. When the skin is deep golden brown and crisp, flip the breasts over and briefly brown on the other side. Place the star anise, ginger and thyme into the rendered fat and then baste the breasts until they have finished cooking, 3 to 5 minutes for medium. Transfer to a cutting board and keep warm. Reserve the duck fat in the pan for the potatoes.
For the parsley salad: Combine the parsley stems and orange supremes in a medium bowl. Toss with the orange juice, a drizzle of olive oil and a pinch of salt and set aside.
For the potatoes: Bring a medium pot of water to a boil and salt it generously. Meanwhile, tourne the potatoes. Trim each end so it’s flat. The length of each potato should be roughly 2 inches. Using a paring knife or bird’s beak knife, make 7 slices the length of the potato until you end up with a football shape. Put each potato in cold water after you tourne it to prevent oxidation.
Add the potatoes to the boiling water and boil until crisp-tender, 6 to 10 minutes. Drain the potatoes and pat dry.
Place a sauté pan over medium heat, add the reserved duck fat and heat until shimmering. Strain through a fine-mesh strainer into a heatproof bowl, then add 1 tablespoon of the fat back to the pan. Add the potatoes and cook, turning often, until light golden brown on all sides. Turn the heat down to low. Season with salt and pepper, then add the thyme and continue to cook, turning the potatoes occasionally, until tender.
Add the breasts to the pan, then pour off any excess fat. Remove the pan from the heat, add the Grand Marnier and flambe. When the flame goes out, return the pan to the heat, add the reserved sauce and heat through. Stir in the parsley and butter, season with pepper, then remove from the heat. Thinly slice the breasts, flesh-side up, against the grain. Place the potatoes on a platter, followed by the sliced duck, fat-side up. Drizzle with the sauce and top with the parsley salad.
Use extreme caution when igniting alcohol. Remove the pan from the heat source before adding the alcohol. Pour the alcohol into the pan and carefully ignite with a match or click lighter. Return the pan to the heat and gently swirl to reduce the flames.