Tip:If stored properly in a cool, dark place, preferably with high humidity, Yukon Golds don't turn brown as quickly as other potatoes once they're cut. Still, if you're prepping the potatoes ahead, it's a good idea to keep them covered in water or coat them lightly with oil.
Cut the potatoes in half, then cut them in thick slices lengthwise, 1/2 to 3/4 inch wide. Stack the slices and cut them in half lengthwise, then cut crosswise to get 3/4-inch-wide pieces.
Heat 4 Tbs. of the oil in a large (11- to 12-inch) skillet, preferably cast iron, over medium-high heat. When the oil is shimmering hot, add the potatoes and stir immediately to coat them with the oil. Sprinkle with the 3/4 tsp. salt and stir again. Fry the potatoes, stirring frequently, until they're tender in the center and nicely browned on the outside, 25 to 30 minutes. (If the potatoes seem to be browning too fast, reduce the heat to medium or medium-low.)
Turn off the heat. Push the potatoes to one side of the pan and pour the remaining tablespoon of oil into the empty space in the pan. Stir the paprika into the oil and let sizzle for about 5 seconds. Stir the potatoes into the paprika oil until well coated. Stir in several grinds of pepper. Taste for salt and add more if necessary. Serve hot.