Place first 10 ingredients in a blender or food processor, and process until smooth. Set aside.
Place 3 cups water in a large saucepan over medium-high heat, and bring to a boil. Stir in quinoa; cover, reduce heat, and simmer 15 minutes or until water is absorbed. Transfer to a large bowl. Drizzle with tomatillo mixture; stir well to combine. Cool.
Add cucumber, radish, and red bell pepper to cooled quinoa mixture; toss gently to combine. Divide salad among each of 6 plates; top evenly with cheese and parsley.