Rub the potatoes with olive oil and salt; prick them a few times with a fork. Place the potatoes on a baking sheet and bake until tender, 50 minutes to 1 hour. Let cool slightly.
Make a slit in the potatoes and scoop out most of the flesh into a large bowl, leaving 1/2 inch behind so the skins hold their shape. To the bowl, add 1/2 cup of the Parmesan as well as the milk, sour cream, melted butter and half of the scallions; fold together to combine. Season with salt and pepper. Divide the mixture among the potato skins, mounding a bit, and sprinkle with the remaining 1/2 cup Parmesan.
Bake the stuffed potatoes until golden brown on top, 15 to 20 minutes. Sprinkle with the remaining scallions.