Preheat a grill to medium. In a bowl, toss 3 quartered plums with 1/4 cup brown sugar, the juice of 1 lemon and a pinch of salt; let sit for 10 minutes. In a 10-inch cast-iron skillet set on the grill, melt 4 tablespoons unsalted butter. Stir in 1 cup fresh breadcrumbs and cook until toasted; stir in the marinated plum liquid. Transfer the mixture to a plate. Place 12 egg roll wrappers on a work surface, pointed side toward you. Spoon 2 teaspoons of the crumb mixture into the center of each wrapper and top with a marinated plum quarter. Brush the edges with water and fold the corners over the plum to enclose. Thread 3 dumplings onto each of four 12-inch skewers. In a bowl, beat an egg with 1 tablespoon water. Brush the dumpling tops with the egg wash and grill on a well-oiled grill grate, flipping once, until golden, about 8 minutes. Dust with confectioners sugar.