Preheat large skillet or comal over medium-low heat for at least 5 minutes. Place two of the flour tortillas on the heated skillet or comal and top each with a 1/4 cup of the cheese and 1/4 cup of the chilorio. Place the other two flour tortillas on top, and let them heat until the cheese starts to melt and the bottom tortillas begin to gently brown. Spread chilorio fat or vegetable oil on top of each, then flip and cook for another minute.
Transfer to plates and serve with slices of ripe avocado and the guacamole or salsa of your choice.