Preheat the oven to 450º F. Scrub sweet potatoes under cold water , dry, poke all over with tines of a fork, and set in a large baking dish that allows for a little space between them. It's fine if they snuggle together in some places.
Rub potatoes with oil, add salt, and bake for 1 hour—turning potatoes once halfway through to prevent burning. They'll get a little caramelized and sugary in parts, and that is just fine (all the better). Set aside to cool once cooked through.
Split each potato down the middle, squash it from both ends to open up the split, and remove flesh—which can be reserved for another use—with a spoon. Lay each sweet potato skin back in the baking dish, flesh side up. Some skins will come totally clean and some will have sweet potato chunks still stuck to them; both are fine. Continue until the skins cover the base of the dish in a layer.
Drizzle heavy cream all over sweet potatoes, enough to create a little pooling under the skins. Salt dish, and top with a scatter of Parmesan shavings. Bake for 20 minutes until cream caramelizes and tops of some skins start browning. Serve warm.