Preheat the oven to 350 degrees F.
Wash and dry the potatoes. Spread a 1/4-inch bed of salt in a baking dish and top with the potatoes. Prick the top of the potatoes. Bake for about 40 minutes, or until the potatoes are cooked throughout.
Meanwhile, make the prosciutto bits.
Place a small saute pan over medium-high heat. Place prosciutto in heated pan. Drizzle bits with olive oil, and cook, stirring. The prosciutto will give off steam for about 5 minutes while it releases its moisture. When the hiss of steam turns to a sizzle, turn the heat down to medium low and cook, stirring occasionally, until the prosciutto bits are crisp, about 25 to 30 minutes.
Using a slotted spoon, transfer the bits to several thicknesses of paper towel to drain. The bits will crisp even more as they cool. (Use immediately or freeze the bits for up to 6 months and warm in a skillet as needed.)
Remove the potatoes from the oven.
Cut an x in the top of each potato, and push in the sides to split open. Divide the prosciutto bits, mascarpone or creme fraiche, and chives among the potatoes and serve immediately.
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