1Combine the first 5 ingredients in a large Dutch oven. Finely chop the white portion of the three green onions; reserve the tops for another use. Add to the potato mixture. Bring to a boil over medium heat; reduce heat, and simmer for 25 minutes or until the potato is tender. Remove from heat; mash the potato mixture.
2Melt butter in a large sauce pan over low heat; add flour, stirring until smooth. Cook 1 minute, stirring constantly. Gradually add the milk; cook over medium heat, stirring constantly, until the mixture is thickened and bubbly.
3Add the white sauce to the potato mixture; cook over low heat until thoroughly heated. Stir in 2 chopped green onions, parsley, and pepper; cover and let stand 5 minutes.
4Ladle into individual soup bowls. Sprinkle each serving evenly with shredded cheese.