Bring broth to a boil in medium saucepan. Add broccoli and onion; cook 5 minutes or until broccoli is tender.
Meanwhile, brown ground beef in small skillet; drain. Gradually add milk to flour in small bowl, mixing until well blended. Add with ground beef to broth mixture; cook, stirring constantly, until mixture is thickened and bubbly.
Add cheese and oregano; stir until cheese is melted. Season with salt, pepper and hot pepper sauce to taste.