Preheat the oven to 425°F with a rack in the center position
Heat the butter, olive oil, shallot, garlic, and rosemary in a small saucepan over medium-low heat until the butter melts and the rosemary is rosemary, about 2-3 minutes
Set aside.Peel the potatoes and place them in a bowl of cold water to prevent them from browning.Slice a very thin layer off one side of each potato
Working one potato at a time, place the potato flat side down
Firmly hold two chopsticks or wooden skewers along the long sides of the potato
Using a sharp knife, thinly slice the potato crosswise until it hits the chopsticks
Using a fine mesh strainer, strain the butter into a small bowl
Place the sliced potatoes in a 12-inch cast-iron pan or 9x13-inch baking dish
Drizzle the potatoes with half of the butter mixture and sprinkle with the salt
Roast until the potatoes are fork tender, 45-50 minutes and beginning to brown.Remove the potatoes from the oven and drizzle with the remaining butter mixture
Turn on the broiler, then return the potatoes to the oven and broil until the edges are crispy, 5-10 minutes more
Remove the potatoes from the oven and sprinkle with the parmesan
Broil until the cheese is browned, 3-5 minutes more
Transfer to a serving platter or individual plates
Serve sprinkled with minced rosemary
