Melt butter in a large Dutch oven or stockpot over medium-high heat; add 1/4 cup chopped cilantro, onion, and next 5 ingredients. Cook, stirring constantly, 5 to 7 minutes or until tender.
Stir in flour, and cook mixture over medium heat, stirring constantly, 7 minutes or until mixture is golden brown.
Add chicken broth, stirring rapidly until blended; add bay leaf. Bring mixture to a boil; reduce heat, and simmer 20 minutes.
Stir in pepper and whipping cream; cook 5 minutes.
Pour mixture through a wire-mesh strainer into a bowl, discarding vegetables.
Add shredded Monterey Jack cheese and remaining 1/4 cup chopped cilantro.
Pour soup into individual serving bowls. Spoon Black Bean Salsa in center of each bowl.