In a 4-quart slow cooker combine hominy, beans, broth, salsa, and oregano. Cover; cook on low-heat setting for 7 to 8 hours or on high-heat setting for 3-1/2 to 4 hours.
With 30 minutes of cook time remaining, increase to high-heat setting if necessary. In a small bowl stir together cream and flour until smooth; stir into mixture in cooker. Cover; cook for 30 minutes more or until mixture is slightly thickened.
To serve, ladle soup into bowls. Top with green onions and shredded cheese, if desired.