For carrots, in a resealable plastic bag combine carrots, the 3 Tbsp. orange juice, 2 tsp. agave nectar, and ½ tsp. salt. Squeeze out as much air as possible, seal bag, and let stand at room temperature while preparing dressing and salad, about 1 hour. Drain before adding to salad.
For dressing, in a blender container combine 3 Tbsp. orange juice, the egg yolk, vinegar, Worcestershire sauce, mustard, the 1 tsp. agave nectar, the garlic, ½ tsp. salt, and the pepper. Cover; blend on low until smooth. With blender running on low, slowly add oil through the feed tube in a steady stream until mixture thickens, stopping to scrape down sides as needed. Transfer to a bowl. Cover; chill until ready to use.
For salad, in a large saucepan combine potatoes, ¼ tsp. salt, and enough cold water to cover. Bring to boiling; reduce heat. Simmer, covered, 15 minutes or until potatoes are just tender. Drain well; cool slightly.
In a large bowl combine 1 cup of the dressing, the red onion, parsley, relish, and green onions. Stir in potatoes, drained carrots, and beets. Fold in eggs. Cover; chill at least 1 hour before serving. If you like, serve with remaining dressing.
