Mix together the oil, oregano, and aji to form a paste.
Spread the paste over the cheese slices.
There is a certain amount of technique to successfully grilling cheese. An essential is that the grill must be very hot. To cook directly on the grill, first set the prepared cheese slices out at room temperature for a couple of hours. As the surface dries out, a hard film starts to form. This is what will keep you from ending up with a gooey puddle in the bottom of your grill. If you don't quite feel up to cooking the cheese directly on the grill, you can use a pie plate or aluminum foil.