Preheat oven to 450°. Bring potatoes and water to cover to a boil in a large saucepan over medium-high heat. Reduce heat to medium-low, and simmer 15 to 20 minutes or until fork-tender. Drain and cool completely (about 20 minutes).
Toss together okra, 1 Tbsp. olive oil, 1 tsp. salt, and 1/2 tsp. pepper, and place in a single layer in a jelly-roll pan. Cut potatoes in half, and toss with remaining olive oil, salt, and pepper. Place potatoes in a single layer in another jelly-roll pan.
Bake okra and potatoes at 450° for 20 to 25 minutes or until tender and golden brown. Remove from oven, and let stand 5 minutes.
Cut okra pods in half lengthwise. Toss together potatoes, okra, vinaigrette, and green onions in a medium bowl. Serve immediately.