Combine the cider, apples, 2 shallots, 2 tablespoons vinegar, 1 teaspoon curry powder, and salt and pepper to taste in a saucepan and bring to a boil. Cook until the liquid evaporates, about 12 minutes; let cool slightly. Stir in 2 tablespoons chopped cilantro.
Meanwhile, pulse three-quarters of the salmon in a food processor until finely ground. Add the remaining salmon; pulse until chopped. Transfer to a bowl; stir in the panko, mayonnaise and the remaining shallot, 2 tablespoons cilantro, 1 tablespoon vinegar and 2 teaspoons curry powder. Add salt and pepper. Form into four 1/2-inch-thick patties.
Melt the butter in a large nonstick skillet over medium-high heat. Add the patties and cook until browned and cooked through, 2 to 3 minutes per side. Butter the buns and sandwich with the salmon burgers, mayonnaise, the apple relish and more cilantro. Serve with chips.
Photograph by Antonis Achilleos
Courtesy of Food Network Magazine