We heat our 10-inch non-stick skillet with half the oil and butter over medium-low heat. We add the potatoes and smush them down with a spatula. We cook without disturbing for 10 minutes, check how it is browning with our spatula, and continue to cook for another 5 minutes.
Meanwhile, we rinse and trim our scallions. The light and some of the dark parts of the scallions are sliced and reserved on the cutting board.
When the underside of the potato pancake is nicely browned, we slide it to a dinner plate and then flip to another plate. The remaining butter and oil is heated and half the scallions added. Some salt and freshly ground black pepper is added to the pan and the pancake is carefully slid back in the pan. We cook for an additional 10 minutes or so. We want both sides of the pancake crisp and nicely browned.
We slide the cooked potato pancake onto a serving plate, sprinkle it with salt and pepper, and spread on the remaining scallions. We cut the pancake into wedges and serve.