1. In large saucepan, melt butter over medium heat. Add potatoes and onion and cook, stirring, until onion is tender, about 5 minutes.
2. Add flour and cook, stirring, for 2 minutes longer.
3. Gradually stir in chicken broth and milk. Bring to simmer and cook until potatoes are nearly tender, about 5 minutes. Add broccoli and cook until broccoli is tender, about 5 minutes longer.