Combine first 4 ingredients in a small saucepan; bring to a boil. Cover; reduce heat, and simmer 15 minutes, stirring frequently.
Remove from heat; let stand 10 minutes.
Place plum mixture in a blender or food processor; process until smooth.
Combine 1 cup boiling water and bulgur in a medium bowl; cover and let stand 20 minutes.
Drain well.
Combine bulgur, pork, 1/2 cup onions, 1/4 cup cilantro, sherry, garlic, ginger, 3/4 teaspoon salt, and pepper in a medium bowl. Divide pork mixture into 12 equal portions, gently shaping each into a 3/4-inch-thick patty. Press a nickel-sized indentation in center of each patty.
Heat a large skillet or grill pan over medium-high heat. Coat pan with cooking spray.
Add 6 patties to pan; cook 5 minutes on each side or until done. Repeat with remaining 6 patties.
Combine remaining onions, remaining cilantro, remaining salt, cabbage, vinegar, and oil; toss gently to coat.