Preheat the oven to 400°F and position a rack in the middle. Line a baking sheet with aluminum foil. Set aside 1 tablespoon of the dark green scallions for garnish.
Pierce each potato several times with a fork, if desired. Place the potatoes directly on the baking sheet, rub them with the oil, and sprinkle evenly with ½ teaspoon of salt. Bake until tender, about 60 to 70 minutes.
Allow the potatoes to cool for 5 to 10 minutes until they can be handled.
Cut each potato in half so the flatter side rests on the baking sheet. Scoop the flesh from each half, leaving about ¼ inch of potato near the skins, and transfer the flesh to a large bowl. Discard 2 of the potato skins and return the remaining 8 skins to the baking sheet.
To the hot potato flesh, add butter, remaining 2 teaspoons of salt, and pepper. Mash until smooth and creamy. Stir in heavy cream, then mix in egg yolks until combined.
Fold in cheese and remaining scallions until evenly distributed.
Spoon the filling evenly back into the potato skins, mounding slightly. Sprinkle with paprika.
Bake again until warmed through and slightly crisp on top, about 20 to 25 minutes.
Garnish with reserved scallions and serve.