Mix broth and soup in a large stock pot. Bring to a boil over medium-high heat. Add broccoli; return to a boil and reduce heat. Simmer, covered, for 5 minutes or until broccoli is tender.
Heat butter in a medium skillet over medium heat; add onion. Saute until tender, about 5 minutes. Add flour. Cook for 1 minute longer.
Gradually stir milk into skillet. Cook, stirring continually, until thickened, about 5 minutes. Add salt and pepper; mix well.
Stir milk mixture into broccoli mixture. Add Velveeta Cheese. Simmer over low heat, stirring frequently, for about 10 minutes. Ladle soup into a serving bowl. Top with cheddar cheese.
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