Preheat the oven to 350 degrees F. Rub the butter all over the inside of a 12 x 10 x 2 1/2 inch baking tray or roasting pan and set aside.

Slice the potatoes as thin as possible, use a mandolin if you have one and transfer them to a bowl.

Heat the cream, milk and garlic in a pot until it starts to boil and starts to thicken slightly. Take off the heat.

Place one layer of the potato slices in even rows and slightly shingled on the bottom of the baking dish.

Season with salt and pepper and cover with both kinds of the grated Parmesans.

Place another layer of potatoes on top of the first layer going in the opposite direction and season again. Sprinkle more cheese on top.

Repeat with a final layer of potatoes ending with a cheese layer on top. Season again.

Slowly pour the hot milk mixture over the layered potatoes making sure to cover all of them and place in the oven.

Gently press down on the potatoes to make sure the liquid is getting in all the spaces.

Bake for about 60-70 minutes or until the tip of a sharp knife can go through the potatoes and the cheese and cream are all melted.