Position an oven rack in the center of the oven and preheat the oven to 425 degrees F. Shave a thin sliver from one side of each potato to give it a flat surface to stand on while you slice it. Make thin slices into the potato about 1/16-inch thick, stopping before you cut all the way through. (Placing a chopstick on either side of the potato while you slice it can help stop the blade before it cuts all the way through.) Put each potato on a separate sheet of foil. Shape the foil around the potatoes to wrap them, but leave the tops open and exposed. Put the potatoes on a rimmed baking sheet.
Melt the butter in a small skillet over medium-high heat, swirling occasionally, until browned and nutty, 2 to 3 minutes. Stir in the brown sugar, vanilla, cinnamon and salt. Drizzle the butter mixture over the potatoes and pinch the foil together on top to seal the potato inside. Bake for 45 minutes, then let cool for a few moments. Remove the potatoes from the foil, put them on a serving platter and drizzle with the sauce leftover in each foil packet. Sprinkle with the pecans before serving.
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