Combine first 5 ingredients in a Dutch oven; bring to a boil. Reduce heat, and simmer, uncovered, 20 minutes.
Combine flour and milk in a small bowl, stirring until smooth. Add to potato mixture. Cook over medium heat, stirring constantly, 5 minutes or until thickened.
Pour half of potato mixture into container of an electric blender; cover and process until smooth, stopping once to scrape down sides. Pour into a large bowl. Repeat procedure with remaining half of potato mixture.
Return mixture to Dutch oven. Add cheese; cook over medium heat, stirring until cheese melts. Ladle soup into individual bowls; sprinkle each serving evenly with green onion.