I had a quesadilla for lunch today and for a long time I have always been unhappy with they way they are constructed. I guess this is the engineer in me but I will utilize a simple graphic to demonstrate what I mean.

This simple graphic represents the standard way they seem to be made. The red lines represent cuts and the yellow is the filling. You end up with four pieces but the two that have the red arrows pointing to them fall apart since they have no fold. I personally like to put salsa and sour cream inside which makes matters even worse. The two pieces on the edges are much easier to eat and you can even use the fold to scoop stuff into them.
This next graphic represents an alternative way (my possibly but doubtfully original way) to fold them.

Here again the red is a cut and the yellow is the filling. This does add an extra step as you are making two smaller quesadillas but in the end each piece has a fold. I don't think the extra effort is significant but I think the enjoyment would be.