Preheat oven to 220°C (200°C fan-forced). Oil a deep 2-litre (8-cup) ovenproof dish.
Cook broccoli in a large saucepan of boiling water for 5 minutes or until just tender; drain. Rinse under cold water; drain. Cool.
Melt butter in same cleaned pan; add flour. Cook, stirring, for about 2 minutes or until mixture bubbles and thickens. Gradually stir in the milk; cook, stirring, until mixture boils and thickens. Stir in cheddar, chicken and broccoli; season. Spoon mixture into dish.
Tear bread into pieces; combine with remaining ingredients in a medium bowl. Sprinkle bread mixture on top of chicken mixture. Bake for about 30 minutes or until browned lightly. Stand for 5 minutes. Serve sprinkled with extra parsley.