Combine broccoli and broth in microwave-safe covered container and microwave on high for 3 to 4 minutes or until broccoli is just tender. Set aside.
Melt butter over medium–low heat in a 4 quart pot. Add onions and sauté until limp but not browned.
Add flour and cook stirring for about 3 minutes until the flour cooked but not browned.
Stir in cooking liquid from broccoli and milk; cook until mixture starts to thicken.
Add cheese cubes and black pepper, ham and broccoli; stir over medium heat until cheese melts. Heat through but do not boil. Salt to taste. Serve hot.