Preheat oven to 350 degrees F.
Set a large skillet over medium heat and add 4 tablespoons of olive oil. Add sliced onions and cook over medium heat for 10 to 12 minutes until they are tender and brown all over.
Using a mandolin (or sharp knife), finely slice the potatoes into rounds (you can place them in a bowl with a wet towel over the top to stop them from going brown while you work). Place the potatoes into a bowl and season with salt and pepper. When ready, add the onions and toss to combine without breaking potatoes.
Add about 1 tablespoon water to the same pan the onions were cooked in and allow it to come to a bubble. Using layered paper towels, wipe the pan clean.
Add some extra-virgin olive oil to the pan and add the potatoes to the pan, making sure the potatoes are flat. Top with the diced butter.
Take a piece of parchment paper and fold in half. Find the middle of the parchment along the crease and hold in place with your finger. Taking the right side of the parchment, pull it towards the center and fold it straight down to create a diagonal edge. Fold the parchment in half to create a triangle. Place the pointed edge in the middle of the saute pan on top of the potatoes to find its radius. Make a marker of where the pan edge ends (or starts). At this point you can cut the parchment at this marker and open to reveal a circle.
Cover the potatoes with the parchment paper and press down. Drizzle some extra-virgin olive oil over the top so it down burn and rub it in.
Place the pan into the oven on the top rack and bake for about 45 minutes.
When done remove from oven and run a knife around the edge to separate from the pan. Place a large plate on top of the saute pan and flip. Remove the saute pan. Allow to cool slightly before cutting into slices.