Place the sliced potatoes in a large bowl and cover with water. Swirl the potatoes around to release the starch. Drain. Lay the potatoes out on paper towels and blot the top with paper towels so the potato slices are dry.
In a large bowl, combine 4 tablespoons of melted butter, salt and freshly ground black pepper, cornstarch and rosemary. Add the potatoes and toss to coat.
Place a large oven-proof skillet (a cast iron skillet works great) over medium heat and melt the remaining tablespoon of butter. Remove from heat. Layer the potato slices in the pan starting in the center and moving out around the circle, overlapping each slice slightly.
Place the skillet back on the stove top over medium high heat. Cook until the edges just start to turn translucent. Spray a sheet of aluminum foil with olive oil and lay foil, greased side down, on top of potatoes. Put another (oven-proof) pan on top of the foil to press and weight the potatoes down. Transfer to the oven.
Bake for 20 minutes. Remove from the oven and remove the top pan and the foil. Continue to bake for another 20 minutes or until the potatoes are tender.
Carefully slide the galette onto a plate. Place another serving plate on top of the potates and invert the "cake" onto the serving plate, so the bottom side is up. Garnish with parmesan cheese and a sprig of rosemary. Slice into wedges and serve.