Preheat oven to 425 degrees F.

In a small sauce pan over medium-low heat melt the butter with the olive oil, shallot, garlic and rosemary. Set aside.

Peel the Potatoes and place them in a bowl of cold water, to prevent them from turning brown.

Slice a very thin layer off the bottom of each Potato so that they don't roll while slicing them. With the flat side of the Potato down, place 2 chopsticks or wooden skewers on either side and firmly against the body of the Potato (lengthwise). Using a sharp knife, thinly slice the Potato pressing knife down until it hits the wooden skewer. Be careful on the edges of the Potato, not to trim the sides off unintentionally.

Place slices Potatoes back into cold water.

Using a fine mesh sieve, strain the butter into a bowl. Once all the Potatoes are all sliced, place in a 12 inch cast iron pan or 9x13 baking dish. Drizzle Potatoes with 1/2 of the butter mixture. Sprinkle with salt.

Bake in the oven, on middle rack, for 45-50 minutes, until tender when pierced with a fork in the center. This may be a few minutes more or less, based on your oven and the size of your Potatoes.

Remove from the oven and drizzle with the remaining butter mixture. Broil for 5-10 minutes until edges are crispy. Sprinkle Parmesan cheese evenly over the Potatoes. Place the Potatoes back into the oven for 3-5 minutes longer until the cheese is nicely browned.