To prepare relish, combine the first 4 ingredients in a small bowl; set aside.
Preheat oven to 400°.
To prepare soup, combine carrots, sweet potato, and onion on a jelly-roll pan; drizzle with oil. Toss to coat. Bake at 400° for 30 minutes or until vegetables are tender and just beginning to brown, stirring after 15 minutes.
Place vegetables, broth, and ginger in a Dutch oven over medium-high heat; bring to a boil. Cover, reduce heat, and simmer for 20 minutes.
Place half of vegetable mixture in a blender. Remove center piece of blender lid (to allow steam to escape); secure blender lid on blender. Place a clean towel over opening in blender lid (to avoid splatters). Blend until smooth. Pour pureed mixture into a large bowl; repeat procedure with remaining vegetable mixture. Stir in salt and pepper. Ladle 1 cup soup into each of 4 bowls. Stir parsley into relish. Top each serving with 1 tablespoon relish mixture.