Prep. Peel and mince the shallot and toss it into a largish bowl. Peel and slice the garlic as thin as you can and add it to the bowl. Chop the prosciutto into 1/4-inch chunks and in it goes. Mince the rosemary and add it. Scrub the potatoes, cut out the eyes, and slice them very thin, about 1/8 inch thick (a mandoline works great here). Add them to the bowl. Melt the fat and combine it with the potatoes, shallot, garlic, prosciutto, rosemary, and pepper. Toss to make sure all the slices are evenly coated with the aromatic mixture. Grate the cheese and chop the tarragon leaves and set them aside.
Fire up. Preheat your stand-alone griddle on high. Or get your grill to Warp 10 and preheat a large cast-iron skillet or a griddle that can go on top of the grates.
Cook. Scoop the potato mixture onto the griddle and spread into an even layer. Try to get each slice of potato in contact with hot metal. Close the lid and sizzle for about 30 minutes. Putting the lid down helps the potatoes cook through. If you use a large skillet, cover it with a couple lids or a big sheet of foil. Check the undersides after 20 to 30 minutes, and when they get golden, if you sliced them thin, they are done. Taste one to see. It should be tender and not mealy inside. On some griddles, but especially with a cast-iron skillet over a hot grill, you may need to lower the heat so the potatoes don't burn before they are cooked through and tender. Near the end of cooking, if you wish, drizzle with truffle oil and mix it in.
Add the cheese. Scatter the cheese and tarragon evenly over the top and close the lid until the cheese melts, 5 minutes or so. (For a nicer presentation, you can scoop the potatoes into a serving dish, scatter the cheese and tarragon on top, and microwave for 30 seconds.)
Serve. Serve with a large spatula to keep the lovely top intact and scatter with large-grain salt.