Preheat the oven to 350°F. Place potatoes on a rimmed baking sheet and bake for 35 minutes, until tender. Remove from the oven and let cool. Preheat the broiler to high.
Once the potatoes are cool enough to handle, cut them in half and scoop out the flesh with a melon baller or small spoon (be careful not to get too close to the skin).
Transfer the flesh to a medium bowl and add the salt, cheese, yogurt, and milk, and mash with a large fork or potato masher.
Place the potato skins on the rimmed baking sheet. (To get the potato halves to sit upright, slice a bit off the bottoms with a knife.) Brush the potatoes with the oil and stuff each half with 1 to 2 teaspoons of the cheese filling, depending on the size of the potatoes.
Broil for 3 minutes, until slightly golden and heated through. Sprinkle with scallions and serve hot.