Heat a skillet over medium heat. Add the oil and heat until shimmering. Add the potato mixture in an even layer and press down firmly with a spatula to form a compact pancake.
Cook undisturbed for ~8-12 minutes then carefully loosen the edges with a spatula. Place a plate or cutting board over the skillet and carefully flip the hash brown pancake onto it.
Return the skillet to the heat and slide the hash browns back into the pan, crispy side up. Add the butter around the perimeter of the potatoes, and allow it to melt.