Place the shredded potatoes in a large bowl and cover with cold water. Let soak for 5 minutes to remove excess starch.
Drain the potatoes and place them in a clean kitchen towel. Squeeze out as much moisture as possible.
In a large bowl, combine the shredded potatoes, salt, black pepper, garlic powder, onion powder, smoked paprika, and all-purpose flour. Mix well.
Add the beaten egg to the potato mixture and stir until everything is evenly combined.
Divide the mixture into 12 equal portions. Shape each portion into a log about 3 inches long and 1 inch thick.
Preheat the air fryer to 400°F (200°C) for 5 minutes.
Brush each potato log lightly with vegetable oil on all sides.
Place the potato logs in a single layer in the air fryer basket, making sure they do not touch. You may need to cook in batches.
Air fry the potato logs at 400°F (200°C) for 12-15 minutes, turning halfway through, until they are golden brown and crispy.
Remove the potato logs from the air fryer and let them cool for 2 minutes before serving.