The Arizona cheese crisp is defined by treating the tortilla as the thing to be cooked rather than the wrapper for something else. A large flour tortilla is laid flat, covered edge to edge with cheese, and heated directly until the tortilla itself goes rigid and blistered and the cheese fuses to it as a single sheet. This is the opposite of the wrap logic, where a soft tortilla bends around a filling. Here nothing is folded, and the bread is not pliable by the time it reaches the table: it is a crisp, flat disc of cheese-laced dough eaten in shards. The crisp is the point, and the cheese is what makes the crisp possible.
The craft is in driving the tortilla to the edge of burning without taking it there. The flour tortilla is large and thin, and it has to be heated hard enough, on a flat-top, under a salamander, or in a hot oven, that it dries and stiffens into a rigid plane rather than steaming soft. The cheese is spread fully to the rim so that as it melts it bonds to the entire surface and crisps along with the dough at the edges instead of sliding into a puddle in the center. Timing is the whole discipline: pulled early the tortilla is limp and the thing collapses under its own cheese; pulled late the dough scorches and turns bitter. It is served flat and open, cut into wedges like a pie, and eaten immediately, because a cheese crisp that sits loses its rigidity within minutes as steam works back into the dough. Its structural relatives are the quesadilla and the tostada, but it is neither: it is not folded and not built on a fried base, it is a baked or griddled crisp in its own right.
The variations are mostly a matter of what rides on top of the cheese before or after the crisp sets. Green chile is the common Arizona addition, scattered over the cheese so it crisps into the surface. Ground or shredded meat turns it heartier and heavier, which tests how much load a crisp disc can carry before it cracks. A folded version closes the disc on itself and edges toward a quesadilla. Each of those is its own preparation and deserves its own article rather than being crowded in here.