Bring the water to a boil in a medium saucepan. Add wild rice; cover, reduce heat, and simmer 1 hour or until tender. Set aside.
Cook squash in boiling water 4 minutes or until tender. Rinse squash with cold water; drain.
Cut the poblanos in half lengthwise; discard the seeds and membranes. Place pepper halves, skin sides up, on a foil-lined baking sheet; flatten with hand. Broil for 10 minutes or until blackened, turning occasionally. Place in a zip-top plastic bag; seal. Let stand 15 minutes. Peel and chop poblanos. Set aside.
Bring the broth to a boil in a large saucepan. Add the cooked wild rice and Arborio rice; cook 2 minutes, stirring constantly. Reduce the heat to medium, and add the cheese and butter, stirring until the cheese melts. Add squash, poblanos, thyme, salt, and pepper; cook 2 minutes or until thoroughly heated.