Place the duck and fat back in a mixing bowl. In a separate bowl combine sea salt, pepper, sugar, fish sauce, shallots, lemongrass, ginger and garlic. Stir into the meat mixture and mix well. Spread on a rimmed baking sheet, transfer to the freezer, and chill until very cold so that the meat is crunchy on the exterior but not frozen solid. Remove from the freezer and pass through a meat grinder set up with a large die directly into a mixing bowl. Stir in the olives, pine nuts and kale and gently mix to evenly distribute. Spoon 2 tablespoon mixture of the meat mixture into a non-stick frying pan and spread into a thin patty. Cook the test patty over low heat until cooked through. Taste for seasoning and adjust if necessary. Form into a 2-3 ounce patties depending on the size of the buns.
Cook the duck patties over a medium-hot grill over indirect heat for 2-3 minutes a side. Place the patties on the bottom part of the hamburger bun and top with the roast pepper and arugula. Cover with top part of the bun and serve.
Enjoy with a glass of Cakebread Cellars Rubaiyat Red Wine Blend.