In a large saucepan, combine broth, broccoli, onion, and roasted garlic. Bring to boiling; reduce heat. Cover and simmer about 10 minutes or until broccoli is very tender. Place half of the broccoli mixture in a blender or food processor. Cover and blend or process until smooth. Transfer to a bowl. Repeat with remaining broccoli mixture. Return all of the mixture to saucepan.
Bring broccoli mixture to simmering. Add cheese; cook and stir until cheese is melted. Stir in half-and-half and ham. Season to taste with salt and pepper. Makes 4 servings.