Adjust oven rack to upper-middle position, place rimmed baking sheet on rack, and heat oven to 450°F.
Meanwhile, toss potatoes, cornstarch, garlic powder, 3/4 teaspoon salt, and 1/4 teaspoon pepper together in large bowl. Carefully remove preheated baking sheet from oven, add oil, and tilt baking sheet to evenly coat with oil. Place potatoes, cut side down in single layer, on baking sheet. Roast until browned around edges, about 30 minutes.
While potatoes roast, mix butter, garlic, parsley, and zest together in medium bowl. Remove baking sheet from oven and, using metal spatula, turn potatoes skin side down. Roast until potatoes are crisp and deep golden brown, 10 to 15 minutes.