One by one, lay tortillas out and place two slices of Cheddar cheese down the center of each.
Starting with one end that does not have Cheddar cheese close to it, start rolling like you're rolling a cigar. When about halfway, tuck the ends up over the part you've already rolled and some of the cheese, like you're rolling up a burrito. Continue rolling until you reach the other side of the tortilla and the entire thing has been rolled. Repeat with each remaining tortilla.
Heat oil in a non-stick skillet over medium heat. When hot, add the tortillas, seam-side down. Fry for about 5 minutes and then flip, frying for another 5 minutes. If the tortillas start to come undone, place a lid on them that will just fit inside the skillet to keep them closed.