Melt butter in a medium saucepan. Add onion and cook until soft. Add broth, sauerkraut and bay leaf. Cover; reduce heat and simmer for 15 minutes.

In a small bowl, mix cornstarch and water. Add to saucepan; stir in cream, half-and-half, corned beef and cheese.

Simmer over very low heat for 10 to 15 minutes, stirring often; do not boil. Remove bay leaf and add salt and pepper. Ladle into bowls and sprinkle with croutons.