Pour oil to depth of 1/4 inch into a large skillet, and heat over medium-high heat to 350°. Combine potatoes and green onions in a large bowl. Sprinkle with panko, flour, and salt; gently toss. Stir in eggs.
Drop potato mixture, in batches, by 1/4 cupfuls into hot oil in skillet; slightly flatten each with a spatula or fork. Cook 2 to 3 minutes on each side or until lightly browned. Drain latkes on a wire rack over paper towels. Keep warm on a wire rack in a jelly-roll pan in a 200° oven. Serve immediately with Thyme-Scented Applesauce.