Place the eggplant halves in a colander, and sprinkle with salt. Toss well; drain 1 hour. Rinse well, and pat dry.
Place beans in a large saucepan of boiling water; cook 4 minutes. Drain and plunge into ice water; drain. Place beans in a large bowl.
Combine vinegar and next 6 ingredients (vinegar through chile pepper) in a microwave-safe dish, stirring with a whisk. Microwave at HIGH 1 minute.
Heat a large nonstick or cast-iron grill pan coated with cooking spray over medium-high heat. Add eggplant halves to pan; cook 3 minutes on each side or until just tender. Remove from pan. Add onion to pan; cook 3 minutes on each side or until tender. Remove from pan. Cut eggplant halves diagonally into 1 1/2-inch-wide pieces. Coarsely chop onion. Add eggplant pieces, chopped onion, bok choy, and noodles to green beans; toss to combine. Add vinegar mixture, green onion, sesame seeds, and cilantro; toss well to coat.