Combine water and chicken in a 3-quart casserole. Cover with lid; microwave at HIGH 30 minutes or until chicken is done, stirring after 15 minutes. Drain in a colander over a bowl, reserving cooking liquid. Cool chicken slightly. Remove chicken from bones, and discard bones. Shred chicken with 2 forks to measure 2 1/2 cups.
Combine broccoli and next 4 ingredients (broccoli through basil) in casserole. Cover; microwave at HIGH 8 minutes or until tender, stirring after 4 minutes. Add the reserved cooking liquid, chicken, pasta, salt, and pepper. Cover; microwave at HIGH 6 minutes or until pasta is tender. Ladle soup into 6 bowls. Sprinkle each serving with cheese.