1. Melt butter in stock pot on medium, add onion and cook til' soft. Add pepper and garlic, and cook for a few minutes. Add broccoli and chicken broth. Bring to a boil, then simmer to broccoli is tender (10-15 minutes).
2. In separate bowl, whisk flour into milk until completely dissolved. Stir into soup, stirring frequently ti'l thickened. Reduce heat to low, and then stir in cheese til smooth and heated through. Salt to taste.