1 cup sliced carrots
2 cups chopped broccoli
1 cup water
1 teaspoon chicken bouillon granules
1/4 cup chopped onion
1/4 cup butter
1/4 cup all-purpose flour
1/4 teaspoon ground black pepper
2 cups milk
2 cups shredded sharp Cheddar cheese

In a small saucepan over medium-high heat, combine carrots, broccoli, water, and bouillon. Bring to a boil. Cover, reduce heat, and simmer for 5 minutes. Remove from heat, and set aside.

In a large saucepan, cook onion in butter over medium heat until onion is translucent. Stir in flour and pepper; cook 1 minute. Stir in milk. Bring to a boil, then stir in cheese until melted. Stir in reserved vegetables and cooking liquid. Heat through, and serve.