Preheat broiler. In a bowl, whisk eggs, pepper and salt. Stir in 1 cup cheese and ham.
In a 10-in. ovenproof skillet, heat butter over medium-high heat. Add broccoli; cook and stir until tender. Reduce heat to low; pour in egg mixture. Cook, covered, 4-6 minutes or until nearly set. Sprinkle with remaining cheese.
Broil 3-4 in. from heat 2-3 minutes or until eggs are completely set. Let stand 5 minutes. Cut into wedges.