In large skillet, brown sausage; drain. Transfer sausage to large saucepan.
Combine carrots, broccoli and butter in skillet. Saute 5 minutes or until vegetables are crisp-tender; add to sausage. Combine flour and 1 cup milk; add to sausage mixture with remaining milk, chives, bouillon and lemon-pepper seasoning. Heat to boiling, stirring frequently.
Cut cheese into chunks; add to soup. Continue to cook, stirring frequently, until cheese is melted. If soup becomes too thick, thin with additional milk.