Add the oil to a medium nonstick skillet and heat to medium-low. Line a plate with paper towels. Tear the tortillas into bite-size pieces and sprinkle them into the skillet. Toss to coat evenly with the oil and fry them until they are fairly crispy but not burned. Be patient: This can take 15 to 20 minutes. Once the tortilla pieces are nice and crunchy, transfer to the paper towel-lined plate and blot lightly to soak up any excess oil.
Note: You can skip this step and use 1 to 2 handfuls of tortilla chips instead. This is a great way to use stale tortilla chips.