In a 5- to 6-quart slow cooker, stir together soy sauce, sugar, garlic, cilantro, ginger, 1/2 cup scallions, vinegar, coriander, and pepper. Add chicken and carrots; toss to coat. Cover, and cook on low until chicken is tender, about 6 hours. Using a large spoon, skim off and discard any fat from surface of cooking liquid.
In a 2-cup glass measuring cup, whisk cornstarch with 1 tablespoon water. Ladle 1 cup cooking liquid into measuring cup; whisk to combine. Pour into a small saucepan, and bring to a boil; cook until thickened, about 1 minute. With slow cooker turned off, stir in cornstarch mixture. Serve chicken with white rice, and garnish with cilantro sprigs and remaining 1/2 cup scallions.