In a 4-quart saucepan, melt butter over medium heat. Cook onion and garlic in butter 2 to 3 minutes, stirring frequently, until tender. Stir in flour, salt and pepper. Cook, stirring constantly, 1 minute.
Stir in broth, broccoli and corn. Heat to boiling over high heat. Reduce heat; simmer 5 to 7 minutes, stirring occasionally, until vegetables are tender.
Stir in half-and-half. Cook 2 to 3 minutes or until hot (do not boil). Serve and enjoy.