Place poblano chile halves, skin sides up, on a foil-lined baking sheet coated with cooking spray; flatten with hand. Broil 16 minutes or until blackened. Place chiles in a zip-top plastic bag; seal. Let stand 10 minutes. Peel and discard skins; cut chile halves into strips to measure 3/4 cup. Reserve any remaining chile for another use.
While chile stands, cook brown rice according to package directions, omitting salt and fat; drain well.
Preheat oven to 350°.
Cook beef, onion, and garlic in a Dutch oven over medium-high heat until browned, stirring to crumble beef. (Drain if necessary, and return beef mixture to pan.) Add rice, diced tomatoes, and next 9 ingredients. Bring to a boil; cook, uncovered, 3 minutes.
Spoon 3 cups beef mixture into an 11 x 7-inch baking dish coated with cooking spray. Top with chile strips and remaining beef mixture. Bake, uncovered, at 350° for 20 minutes or until bubbly.
Remove from oven; sprinkle with cheese. Cover loosely with foil; let stand 5 minutes or until cheese melts.