Set a large saucepot over medium-high heat. Attach a cooking thermometer to the side of the pot. Then pour 3 inches of olive oil into the pot.
While the oil is heating, peel and chop the potatoes. Place the potato chunks in a colander and rinse well. Then set them out on paper towels to dry. Pat the tops so the potatoes are dry on all sides.
Set a large bowl and the counter and line with paper towels. Then in a small bowl, mix the salt, smoked paprika, garlic powder, and cayenne.
When the oil reaches 300-325 degrees, gently lower a third of the potatoes into the oil, using a skimmer or slotted spoon. Stir and fry for 5-6 minutes, until golden. Remove one chunk and check that the potato is fork-tender in the center. Then remove all the potatoes with the slotted spoon.
Place the fried potatoes in the paper towel lined bowl. Sprinkle one-third of the seasoning mix over the potatoes and toss.
Repeat the frying and seasoning two more times, until all the potatoes are cooked. Serve warm as-is, or with aioli or creamy ranchero sauce.
