Put the breadcrumbs in a large bowl and drizzle the milk over the top; stir and let soak for 5 minutes. Add the ground turkey, parsley, ground ginger, garlic powder, cayenne, 1 teaspoon salt and 1/4 teaspoon pepper. Divide the mixture into 8 portions, roll into balls and pat into patties.
Arrange the patties in a lightly oiled 9-by-13-inch baking dish. Bake for 5 minutes.
Meanwhile, gently warm the cranberry sauce with a few tablespoons of water to loosen.
Spoon half of the warm sauce on top of the patties. Return the cranberry sauce to a simmer and remove from the heat. Return the patties to the oven and continue baking until browned, glazed and cooked through, about 20 minutes more.
Flip the patties and brush them with more sauce while still hot. Let cool slightly, about 5 minutes.
Spoon the remaining cranberry sauce onto the bottom halves of the rolls. Top each roll with a patty and some arugula. Serve warm.