Bring potatoes and water to cover to a boil, and cook 25 minutes or just until tender; drain well. Cool slightly, and cut into wedges.
Whisk together oil and next 4 ingredients in a large bowl; add potatoes, green onions, and feta cheese, tossing to coat. Cover and chill at least 2 hours or up to 8 hours. Sprinkle with parsley before serving. Serve over mixed salad greens, if desired.