Preheat oven to 425 degrees. Heat butter, oil, and garlic over a low heat for 7 minutes until the garlic is infused. Remove garlic cloves and set aside.
Peel potatoes and then slice very thinly on a mandolin or by hand.
Spread half of the infused oil and butter in the bottom of a 10-inch non-stick skillet, making sure to coat the whole pan.
Start layering potatoes on the outside in a circle and work your way in. Sprinkle with ⅛ teaspoon of salt and 1 ½ teaspoons of parmesan cheese. Repeat with next layer.
On the third layer, sprinkle with remaining ⅛ teaspoon of salt.
Transfer the skillet to the stove and turn on to a medium-high heat. Once the potatoes begin to sizzle cook for exactly one minute 30 seconds and transfer to the oven. Cook for 20-25 minutes until potatoes are cooked through.
Remove from the oven, and using a knife release any of the potato that is sticking to the sides of the pan. Put a large plate upside-down over the skillet. Flip the whole thing over very quickly, making sure to keep the plate and skillet close together.
Recipe by Cooking for Keeps at https://www.cookingforkeeps.com/garlic-parmesan-potato-galette/