Preheat broiler to high.
Cook rice according to package directions; drain. While rice cooks, heat a large 12-inch ovenproof skillet over medium-high heat. Add oil to pan; swirl to coat. Add onion, mushrooms, and chicken; sprinkle with 1/4 teaspoon salt and pepper. Sauté 6 minutes or until chicken and onion are done.
Cook broccoli in microwave according to package directions for 3 minutes. Open package to release steam.
Combine milk and flour, stirring with a whisk or fork until smooth.
Stir milk mixture into chicken mixture in skillet.
Cook 2 minutes or until bubbly and thick, stirring frequently.
Stir in remaining 1/2 teaspoon salt, rice, and broccoli. Sprinkle with cheese.
Broil 1 minute or until cheese melts and just begins to brown.
Riff: Try ground beef in place of the chicken.
Riff: Not a fan of broccoli? Try cauliflower, spinach, green peas, carrots, or green beans instead.
Riff: In place of rice, use 3 cups cooked quinoa (1 cup uncooked).