Moisten enough paper towels to wrap around tortillas.
Working in batches of 4, heat the tortillas, wrapped in the barely damp paper towels in the microwave until pliable. Keep them wrapped as you work to prevent them from drying out and becoming brittle.
Sprinkle a little cheese in the center of each tortilla.
With a piping bag, or by hand, spread a layer of potatoes down the center of each tortilla, no thicker than ½”.
Carefully roll up the tortilla and brush with oil.
Place in the air fryer basket.
Repeat with the next 3 and place all in the basket, seam side down, not touching on another.
Set the air fryer to 390 and cook for 7 to 9 minutes, until tortillas are crispy.
Some potato and cheese filling will fall out. Carefully wipe out the excess filling and repeat until all taquitos are made.