Heat the oven to 375°F and grease a 9-by-13-inch baking dish.
Combine the potatoes, ham, cream, 1 cup cheddar, half the scallions, salt and pepper in the dish.
Cover tightly with foil and bake for 35 minutes.
Uncover, stir from the center to the edges and scatter the remaining cheddar over the top.
Bake uncovered for 25 to 35 minutes, until the potatoes are tender, the cream bubbles thickly around the edges and the center reaches 165°F.
Rest for 10 minutes and add the remaining scallions before serving.