Preheat the oven to 375 degrees F. Rub the potatoes with the oil and season generously with kosher salt. Place on a baking sheet and bake until the potatoes are very tender on the inside and crisp on the outside, about 1 hour, 15 minutes. Let stand 5 minutes.
Meanwhile, heat the butter in a large nonstick skillet set over medium heat. Add the leeks and season with salt and pepper, cook until soft, about 6 to 8 minutes. Add the garlic and thyme and cook until fragrant, 1 minute. Cool slightly.
Cut lengthwise, opening down the center of each potato, stopping about 1-inch from each end. Scoop out the insides into a large bowl, keeping about 1/4-inch shell of potato next to the skin.
Add the leek mixture, cream cheese and milk to the potato and mash well with a fork until combined but slightly chunky. Stir in the chopped parsley. Spoon the filling back into the potato shells, about 1/2 cup of filling for each potato and place back on the baking sheet.
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