Position oven rack at the lowest level. Preheat oven to 450F.

Cover potatoes with cold water in a medium saucepan. Cover and bring to a boil. Drain and refresh with cold water. When cool enough to handle, grate the potatoes. Transfer to a bowl. Add scallions, salt and pepper; toss with a fork until mixed.

Coat a 10-inch pie plate or cast-iron skillet with nonstick cooking spray. Brush 1 teaspoon oil evenly over the surface. Spread half of the potato mixture evenly over the bottom of the pan. Sprinkle with ham and cheese. Spread the remaining potato mixture over top, pressing evenly. Brush the remaining 1 teaspoon oil over the surface. Bake until the underside is golden and the potatoes are tender, about 30 minutes.

Carefully loosen edges with a thin metal spatula or a knife. Shake the pie plate or pan to be sure the potatoes are sliding freely. Invert a serving platter over the pie plate or pan. Grasp the platter and the baking dish with oven mitts and carefully turn over. Remove the pie plate or pan. Cut into wedges with a serrated knife. Serve hot or at room temperature.