Preheat the oven to 180 °C. Soak the cranberries in water. Trim most of the fat from the duck breast. Drain the cranberries and grind them with the pine nuts and a tablespoon of olive oil. Season with salt and pepper. Brush the duck breast with the paste and place the meat in a baking dish. Place in the oven for 12 to 15 minutes.
Coarsely chop the pak choi and sauté in some olive oil. When the vegetables are cooked, add a dash of soy sauce and season with black pepper.
Remove the duck breast from the oven and let rest for a while. Cut the meat into thick slices. Do so carefully so that the cranberry crust remains firm.
Serve with the braised pak choi.