1. Preheat the oven to 400 degrees F (use a convection oven if you have it). Peel the potatoes. Make 1/8-inch repeated crosswise cuts that go almost all the way through each potato. (Set a chopstick or thin wooden spoon crosswise to your knife next to the potato to keep from cutting through the potato.)
2. Heat 2 tablespoons butter in an ovenproof skillet over medium-high heat. Turn the potatoes to coat with butter and sprinkle with 1 teaspoon each salt and pepper. Cook the potatoes until they are golden on the bottom, about 3 minutes. Add 1/3 cup water, bring to a low boil, reduce the heat, cover, and transfer to the oven. Bake the potatoes for 45 minutes.
3. Meanwhile, mix the herbs with the remaining 2 tablespoons butter. Uncover the potatoes, fan the potatoes slightly to separate the slices, and brush evenly with the herb butter. Sprinkle with the Parmesan. Increase the temperature to 450 degrees F and cook uncovered until golden brown, about 15 minutes.
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