Melt the butter with the oil in a large skillet over medium-high heat. Add the potatoes and spread evenly in the pan. Cook undisturbed until the potatoes are golden brown on one side, about 5 minutes.
Carefully turn the potatoes to ensure even browning and add the onion to the skillet. Continue cooking, turning the potato and onion mixture every few minutes, until the potatoes are well browned and the onion is softened and carmelizing, 10 to 15 minutes longer.
Season with salt and pepper to taste and serve immediately.