In a large pan, heat the oil and butter on medium heat.

Add one of your tortillas

Pile on the cheese.  Make sure you have enough cheese to get close to the edges of the tortilla.  The cheese will act as the glue to keep you quesadilla together.  

Top the cheese with another tortilla.  At this point, check to see if the bottom half has crisped up to your liking.  If it has, the quesadilla is ready to flip over.  Using a large spatula, flip the quesadilla over.  Cook the bottom part until the desired crispness, and you are ready to serve.