Soak mushrooms in hot water 30 minutes; drain, reserving liquid. Rinse mushrooms in cold water; pat dry. Remove and discard stems; thinly slice tops. Pour reserved liquid through a fine wire-mesh strainer into a measuring cup; reserve 1/2 cup.
Slice green onions, separating green tops from white portions. Set aside.
Remove excess fat from chicken. Cut chicken into 1-inch cubes.
Sauté chicken in 2 tablespoons hot oil in a large skillet 5 minutes or until done. Remove from pan; cool. Coarsely chop chicken. Set aside.
Sauté white portion of green onions and serrano pepper in remaining 2 tablespoons hot oil in a large skillet 1 minute; add mushroom liquid, curry paste, coconut milk, and soy sauce, and bring to a boil. Reduce heat, and simmer 3 minutes. Stir in mushrooms, carrot, and next 3 ingredients; simmer 3 minutes. Stir in chicken.
Whisk together cornstarch and cold water until smooth; stir into chicken mixture. Bring to a boil over medium heat, stirring constantly; boil, stirring constantly, 1 minute. Stir in basil and green onion tops. Serve over romaine lettuce leaves.