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Preheat the oven to 400°F and set an oven rack in the middle position. Line a baking sheet with aluminum foil. Set 1 tablespoon of the dark green scallions aside to use as a garnish.
Prick each potato a few times all over with a fork, if you like (see note). Directly on the baking sheet, rub the potatoes with the oil and sprinkle all over with ½ teaspoon of the salt. Bake until tender when pierced in the center with a sharp knife (or until the center of the largest potato registers 205°F to 210°F), 60 to 70 minutes. You can also squeeze the potatoes to see if they are soft (be careful; they're hot!). Let sit until cool enough to handle, 5 to 10 minutes.
Using a sharp knife, cut each potato in half so that the flatter, wider side will sit flat on the baking sheet. Scoop the flesh from each potato to within about ¼ inch of the skins, and transfer the flesh to a large bowl. Discard 2 of the scooped potato skin halves (preferably the least perfect ones), and place the remaining 8 potato skin halves back on the baking sheet.
Add the butter, remaining 2 teaspoons of salt, and pepper to the hot potato flesh in the bowl. Using a potato masher or large fork, mash until the butter is melted and the potatoes are broken down. Add the heavy cream and mash until the cream is incorporated and the potatoes are creamy. Add the egg yolks and mash until evenly combined. Using a spoon, stir in the cheese and the remaining scallions until evenly combined.
Spoon the filling evenly into the potato skins, mounding slightly in the center. Sprinkle with the paprika. Return to the oven and bake until the filling is heated through and slightly crisp on top, 20 to 25 minutes. Sprinkle with the reserved scallions and serve.
Note: Conventional wisdom says that prior to baking, you have to prick potatoes with a fork a few times to allow steam to escape during baking. The theory is that if you don’t prick the potato, the steam can build up under the skin and cause the potato to explode in the oven. I don't prick my potatoes and have never had a potato explosion, but pricking won't harm the potatoes, so go ahead and prick them as insurance, if you like.
Make-Ahead/Freezer-Friendly Instructions: The potatoes can be stuffed ahead of time and refrigerated in a covered container for up to 2 days. When ready to serve, heat in a 400°F oven until the filling is warm throughout and crisp on top, 25 to 30 minutes. The stuffed potatoes can also be frozen in an airtight container for up to 3 months. Bake in a 400°F-oven directly from the freezer until hot throughout and crisp on top, 30 to 35 minutes.