1. Preheat oven to 375°.
2. Combine milk and water in a medium saucepan; bring to a boil. Add rice; cook 10 minutes. Remove rice; keep warm. Return milk mixture to a simmer. Add broccoli; cook 5 minutes. Drain; discard milk mixture.
3. Heat a Dutch oven over medium-high heat. Coat pan with cooking spray. Add onion, celery, and bell pepper; sauté 5 minutes. Add cream cheese and processed cheese, stirring until cheese melts. Remove from heat; stir in rice, broccoli, chicken, salt, and black pepper. Spoon 1 cup rice mixture into each of 4 (10-ounce) ramekins coated with cooking spray. Sprinkle each serving with 1 tablespoon Parmesan. Bake at 375° for 10 minutes or until cheese melts.