1. Combine first 7 ingredients in a saucepan. Bring to a simmer; cover and cook 15 minutes or until plums are tender. Discard star anise and cinnamon. Cool completely. Place in a blender; process until smooth.
2. Combine mirin, ginger, soy sauce, and garlic in a saucepan over medium heat. Bring to a simmer; cook 4 minutes or until reduced to 1/4 cup.
3. Trim excess fat and connective tissue from livers; separate livers into lobes. Pat livers dry with paper towels. Heat a grill pan over high heat. Coat pan with cooking spray. Add half of livers to pan; cook 7 minutes or until slightly firm (like a cooked chicken breast), turning once. Remove from pan; brush with half of glaze. Repeat procedure with remaining livers and glaze. Serve with plum sauce and cucumber.